#Linear Inequalities notes

[class11maths]

Linear Inequalities — Class 11 Maths Course by Mathyug

Understanding Linear Inequalities is a fundamental aspect of Class 11 Maths, laying the groundwork for various advanced topics in algebra and calculus. Mathyug’s course on Linear Inequalities is designed to make this topic engaging and easy to grasp, ensuring students not only master the concepts but also apply them effectively in problem-solving scenarios.

Why Choose Mathyug for Linear Inequalities?

Mathyug stands out for its structured approach and comprehensive coverage of topics. The Linear Inequalities module is no exception. Here’s what makes it unique:

High-Quality Video Lectures: Each concept is explained in detail, breaking down complex ideas into simple, understandable steps. The use of real-life examples helps in visualizing abstract mathematical concepts, making the learning process intuitive and engaging.

Detailed Notes: Mathyug provides meticulously crafted notes that complement the video lectures. These notes cover all the theoretical aspects, important formulas, and shortcuts, ensuring a solid understanding of the topic.

Assignments for Practice: The course includes a variety of assignments for linear inequalities that challenge students to apply what they’ve learned. These assignments are curated to cover a broad spectrum of problems, from basic to advanced levels, fostering a deeper understanding and preparing students for exams.

Conceptual Clarity: The focus is on building a strong conceptual foundation. This is crucial as Linear Inequalities form the basis for several other topics in mathematics, including linear programming and calculus.

Course Highlights

Comprehensive Coverage: The course covers all NCERT topics as well as additional concepts required for competitive exams like JEE.

Interactive Learning: The lectures are interactive, encouraging students to think critically and solve problems in real-time.

Regular Updates: Mathyug ensures the content is up-to-date, incorporating the latest syllabus changes and best teaching practices.

Sample Video Showcase

To give you a glimpse of the quality and style of teaching, here’s a sample video from the Linear Inequalities course. This video demonstrates Mathyug’s approach to making complex topics accessible and interesting. It’s a must-watch for anyone looking to excel in Class 11 Mathematics.

Why Linear Inequalities Matter

Linear Inequalities are more than just an academic requirement. They are essential in understanding and solving real-world problems involving constraints and optimization. Whether you’re calculating budget limits, analyzing business profit margins, or simply planning your daily schedule, the principles of inequalities are at play.

Conclusion

Mathyug’s Linear Inequalities course for Class 11 is an excellent resource for students aiming to master this topic. The combination of engaging video lectures, comprehensive notes, and challenging assignments makes it an ideal choice for both regular curriculum studies and competitive exam preparation.

If you’re looking to strengthen your grasp of Linear Inequalities and ace your exams, Mathyug’s course is the perfect companion on your learning journey.

[lipshits-continuous]

Topological Spaces 1: Introduction and Metric Spaces

Welcome to the first of several posts about general topology! The goal of these posts is to give an overview and introduction to key concepts in topology. I will try to give intuitions about definitions and results so that even if you're not as aquainted with formal mathematics you can still get something from this. Whilst there aren't any prerequisties per say (for the reason above), for those who are interested in the moral formal aspects it will be helpful to be familiar with real analysis. Some familiarity with linear algebra is also helpful in this post though probably won't play a role going forward.

Topology is such a broad subject that assigning one goal is quite hard. One early goal is to generalise the notion of continuity and other familiar notions, which we shall do. Topology certainly doesn't stop there. One large goal is to find properties which are invariant under homeomorphism (bijective continuous maps whose inverse is also continuous). We shall see some examples of this as we go further!

The goal of this post is to give context to the definitions of topological spaces and continuity via the study of metric spaces. The definition of a topological space can seem quite dry and like it's been plucked out of thin air when just presented without motivation. In this sense, metric spaces are the bridge between familiar concepts in real analysis and the more general setting of topology.

1.1: Metric Spaces:

As the name might suggest, metric spaces are sets with an appropriate notion of distance between points in the set. For the real numbers, we have an intuitive sense of distance between two numbers: the absolute value of their difference. From this, we can immediately get three desirable properties we'd want a notion of distance to have:

Positivity: |x-y|≥0

|x-y|=0 if and only if x=y

Symmetry: |x-y|=|y-x|.

These are desirable because this says, in order, that distance is always positive, two points are the same only when the distance between then is 0, and the distance beween x and y is the same as the distance between y and x.

The last property is not as immediately obvious from the definition but is still a fairly intuitive property that we'd expect a notion of distance to have: the triangle inequality. Formally, for any x,y, and z real number we have |x-y|≤|x-z|+|z-y|. This just says that the distance between two points is always shorter than the distance achieved by adding an intermediate point. The name comes from visiualising this with lengths of a triangle! The proof that this holds for the absolute value can be found here.

You might ask whether there are any more properties we'd like but it turns out that this is enough to generalise a lot of concepts in real analysis in an appropriate way. That is, we still maintain a lot of nice results without requiring too many rules. So let us finally see the definition!

Definition 1.1:

Note: It's common to combine the first two axioms together but for the sake of clarity, I have separated them.

Examples 1.2:

The details of why each of these is a metric can be found in this post.

A result of the second example is that metric spaces are also an appropriate generalisation of normed vector spaces. The fact they are a generalisation is seen from the fact that the discrete metric cannot be seen as the result of a norm and isn't restricted to vector spaces.

1.2: Continuity:

Intuitively, continuous functions are ones that don't have gaps or sudden jumps. In the case of functions from the real numbers to itself, we can view this as "we can draw its graph without lifting the pencil". This can be restated as "points that are close to each other remain close to each other after the function is applied". But how does one formalise "closeness"? With distances of course!

Definition 1.3:

Remark: Continuity departs on the metrics. A function that is continuous in one metric isn't necessarily continuous in another.

Examples 1.4:

Now I'd like to prove a fairly common result to further demonstrate continuity.

Proposition 1.5:

1.3: Open Sets in Metric Spaces

Now we shall see the first aspects of topology creeping in. One way to think about open sets which don't have any points "at the edge". This is immediately clear in the definition we will give below but when we generalise the notion of an open set, we will seemingly lose this. However, we will see that this intuition will still hold!

Definition 1.6:

Example 1.7:

We will now define the notion of an open set using these open balls.

Definition 1.8:

This does indeed formalise "no points at the edge" since for open sets, all points close enough to x are always in U.

Remark: Openness depends on the metric. For example, {0} is open in the real numbers with the discrete metric but not with the absolute value metric.

Now, "open ball" would be a silly name for it if they weren't indeed open in the sense of definition 1.8 but luckily they are!

Proposition 1.9:

Example 1.10:

Open intervals of real numbers are indeed open with respect to the absolute value. If we have the open interval I=(a,b) for finite a<b, we may view I as an open ball by setting x=(b+a)/2 and r=|b-a|/2. Then I=B(x;r).

Now we shall prove a very important result about open sets that lets you build new open sets out of old opens but will also be the foundation upon which we generalise the notion of open sets!

Lemma 1.11:

Proof:

Remark: Finiteness is important for 3. If we consider the real numbers with the absolute value metric then (-1/n,1/n) is open for all (non-zero) natural numbers. However their intersection over all n is {0} which is not open in this metric.

Typically, courses would usually talk about closed sets now. However, since the discussion doesn't vary much between metric spaces and topological spaces, we will hold off for now.

1.4: Continuity in terms of open sets

This is a very important step in our journey in generalising continuity. This section with along with the next section will suggest that open sets are actually the structures we'd like to study!

Lemma 1.12:

Before we prove this, I'd like to just comment on why this still alligns with our intution about continuity. The right hand side is saying that points end up close together in Y must've been close together in X.

Remark: It is important to note that U open in X does not necessarily imply f(U) is open in Y when f if continuous. For example, take f(x)=x² in ℝ with its usual notion of continuity, then (-1,1) is open but f((-1,1))=[0,1) which is not open. Maps for which open sets are mapped to open sets are called open maps.

We will see examples of how to use the property on the right hand side in the next post!

1.5: Equivalent Metrics

The goal of this section is to see that sometimes different metrics will give rise to the same open sets!

Definition 1.13:

Example 1.14:

I will omit the details of the proof for brievity. Not that the 2 on the right hand side comes from the fact we're in ℝ² and isn't related to the 2 in the metric.

Remark: Not all metrics are equivalent. The discrete metric and d₂ are not equivalent metrics.

Proposition 1.15:

Corollary 1.16:

This ultimately means that some metrics generate the same open sets. Then Lemma 1.12 tells us that equivalent metrics give the same continuous funcitons since we can view continuity in terms of open sets. This suggests that what really matters here is which sets are open. This is what we shall exploit to generalise continuity even further! But that shall have to wait til the next post!

[rins-batcave]

ello ello ello

I asked Mickle Pickle “should I send a pic to rin of you?” And he bit me so sadly no cat pic 4 u today

but u can have some math notes instead

I don’t understand what’s going on on the page

Yum math I like linear inequalities:3333

[neet-aspirant]

28–11–2023, Tuesday

second studyspo of the day lol :") had a productive day today.

made bio notes for 2 hours

solved linear inequalities for an hour

attended a physics lecture for 2 hours

prepared some notes for my chemistry practical exam which is on 19th December (ik it's far away but it's never too early to start right)

2 hours of French lesson on Duolingo (guys you won't believe it's going so well, i'm so excited!!! Je suis une fille. Je suis Meha. :D )

[study-with-aura]

Friday, April 24, 2025

I ended up deciding to volunteer for only two hours today instead of my usual three, so I could still go today but have an extra hour to complete things. I don't know whether I will be posting tomorrow or not, as we are having a sleepover at my place for the GS Seniors to work on a badge. It's one that we have to complete at night, so it makes it easier to have everyone stay over at our place since we hold our meetings here, and we have the extra space. It's only H, E, and me, and they usually sleep in my bed with me since it accommodates the three of us. But the extra bathrooms are the helpful part. I'm excited for the sleepover since we haven't had one in a while. We didn't do it during cookie season this year since we did our cookie season a bit differently than last year. The other levels still did the booth, but we did regular word of mouth as it was easier this time around.

I also got my lit book from the library, so I can start doing physical notes with post-its. While I can't highlight in it like I do on the ebook, this is easier to see visually all at once rather than trying to scroll through all of my notes. Plus, it's kind of fun. I did decide on my literary analysis topic (working title): Haunted by Slavery: Gothic Horror and Moral Decay in Uncle Tom’s Cabin. I wanted to focus on comparison to Gothic literature since there are a lot of gothic elements in the novel, but I also really liked the moral hypocrisy aspect of it, where slaveholders twist the Bible to fit the context they want rather than reading it in the context of the Biblical period itself and the actual moral values the Bible teaches. There is so much Christian hypocrisy happening in this novel when focused on the South (but even in the North through Ophelia) that it felt too good a topic to ignore. And in a way, it does fit the gothic style as well because they use Scripture as psychological entrapment and to condone the evilness of slavery by saying that God wanted it this way, which is not true at all if you actually know the Bible. So I've combined the two.

My current working thesis: In Uncle Tom’s Cabin, Harriet Beecher Stowe employs Gothic conventions within the Southern plantation setting to construct a landscape of psychological torment and moral decay. This literary framework allows her to critique the institution of slavery not only as a system of physical oppression, but also as a reflection of the spiritual and ethical contradictions embedded in antebellum society.

Thoughts? Does it sound interesting to you? My mom is an English/French lit university professor, so I never feel I'm quite meeting her standards, but that's my perception, not hers. Plus, I'm still in high school. I think it's okay if I'm not writing at the college level just yet, since I still have two more years to go, but I am very excited about this topic! 🦄

Tasks Completed:

Algebra 2 - Reviewed systems of linear equations and inequalities

American Literature - Vocabulary quiz (100%) + copied vocabulary words + read about transitions + continued working on the final project

Spanish 3 - Read more about informal commands + practice quiz + completed virtual worksheet

Bible 2 - Read Mark 3

Early American History - Read about the impeachment of Johnson + worked on my final paper

Earth Science with Lab - Completed Milky Way lab + completed virtual lab report

PE/Health II - Read an article on what happens in the brain when the mind blanks

Art Appreciation - Completed daily critiquing assignment on Paul Cézanne's The House with Cracked Walls + read about the painting + jotted down notes about how to recognize a Cézanne, his style, and his philosophy + reviewed artists to this point

Khan Academy - Completed Algebra 2 daily mastery challenge

Duolingo - Studied for approximately 15 minutes (Spanish + French + Chinese) + completed daily quests

Piano - Practiced for two hours

Reading - Read chapters 36-40 of Uncle Tom’s Cabin by Harriet Beecher Stowe (second read-through)

Chores - Vacuumed my bedroom, the study, and the front room + swept and mopped the kitchen floor

Activities of the Day:

Personal Bible Study (Proverbs 4:23)

Group Bible Study (1 Chronicles 3-5)

Volunteered 2 hours at the mission

Ballet

Variations

Journal/Mindfulness

[kanthia]

5DS!!!!! The plot is incredibly fun and introduces some of my favourite archetypes/gimmick cards, I hope you have a blast with it.

On a related note, how'd you end up doing with GX season four in the end? I had a joke in mind about the final stretch being somehow worse than the whole survival horror murder-brainwashing shenanigans going on in season three, but upon further thought I think they're traumatising in such disparate directions that I can't compare them on a linear scale.

(Crowler's spotlight episode genuinely hits hard to the teacher part of my brain, though, even thinking back sixteen (!!) years on. It's good!)

seto kaiba would be so proud that his two legacies are a) crippling socioeconomic inequity and b) an infinite energy source powered by card games and dragons?

unfortuntely the sub of yugioh gx couldn't quite pique my interest; I may still return to it someday. I think to me there's an element of campiness to these old series that I enjoy most in their dubs. (that or I have no taste lol. my favourite season of digimon is the dub of frontier)

thus in my mind jaden yuki never graduated from high school. he went to space, became an evil god, gave zane truesdale incurable heart disease, and then died. yugioh gx fucking rules

[rmfantasysetpieces1]

Atletico Madrid vs Real Madrid +Lille vs Dortmund

Lille has a battle, it is all even so whomever wins this match will proceed and face Barcelona.

Lille is doing better domestically, but this is a battle, the question is which team will raise their quality or diminish quality on the second round. Lille has been more consistent in their domestic league so I argue lille should have a more consistent quality compared to dortmund, but the pitch will display what pans out.

Atleti can defeat real madrid by two goals. Is that the odds of what will happen? no.

The problem atleti have is real madrid have in viniciusjr/mbappe/rodrygo/bellingham/valverde/camavinga are six players who can dribble on their own from the halfway line to goal which means against most teams they have an automatic one on one advantage and against atleti who are not collectively fast it is a huge athletic advantage so atleti have to play a perfect skill game. It is about execution. Atletico madrid players are tired, but these matches define a squads abilities, whether they become legend or just a note.

For me the biggest strategic issue atletico madrid have is conversion rate. Atleti still require too many attempts to score. If atleti can have an uncommon high conversion rate game, we can win. And when I say rate of scoring I don't mean the way most suggest it. for example, if a free header is taken, that is an opportunity to score, but usually that is marked as a non strike if off target, which is false recording for me. Sitters are marked for me. too often the records keepers suggest only what is on target from a strike is an attempt but I oppose that statistical definition. When a low cross goes across the box that is for me an attempt on goal, the fact that a teammate wasn't there is a miss not a non attempt on goal. So atleti based on my view, have to convert chances, not merely strikes on target, but strikes off target, low crosses untouched, these are all chances that need to be converted.

LILLE DORTMUND

IShmaely!

Jonathan David, took a deflection, and david is a player that hasn't been offered a big contract. but he is up, i like david for my Atleti if they have the money

11:15 it is funny abut muenier and bakker, two wide backs who didn't work out at the experienced players at lille are quite the journeyman players

21st the handball check is criminal by the video assisted referee, int he prior situation both teams have tons of players clustered together around chevalier the lille keeper, how can a ball in that chaos be a handball, and if that is how the rules must be then every handball has to be called or lead toa yellow and everyhand ball isn't

28:59 yeah i know genesio ,wonderful set piece, the header across had to be linear and sharp for the secondary header, lille players were in place

circa 34th minute benjamin andre, captain, got to score

wha was the difference between the foul from the dortmund player to the lille circa 47:10 as oppoed to the one from can on davis less than a minute before

circa 53:28 should had been a dive on guirassy that is the problem with video assistance and goal line technology, the focus on certain rules misses that all calls are important equally all over the pitch, in this match, the referee has let harder contacts especially from dortmund to lille go but then lets a dive go.

65:28 ahh lille tired

well here is the problem, Jonathan David has to hold up the ball better.

66:30

akpom on for cabella

gudmonson for ismaely

81:20

the same assholes who complain about morality in the game then try to suggest their teams are inequally done

alot of assholes, some in sportsburstfans see to forget the job of the referee is to call a play not talk about players attitdues or count how many times a player is supposed to do this or that, the job of the referee is to call plays as they see it, the people who complain the most about inequal refereeing then condone it in false views

ATLETICO MADRID VS REAL MADRID

well, simeone is playing the two most athletically capable players at wide back, llorente doesn't pass or dribble well, but recovers and defends well, and is an excellent one two player. Reinildo likes to lock. Gallagher will mark a midfielder, barrios similarly, pressing and trying to move the game forward. Depaul has a huge role for his assists. Griezzman will drop into midfield and support, Simeone plays the wide role and connects with llorente for the one two striaght attack.

The keys for atleti are

have a high conversion rate, you have to score chances, al strikes on target even if not fast

have a low passing interception rate, kick the ball away , you don't have to play low

Alvarez

Griezzman/alvarez/Simeone

Gallagher/Depaul/Barrios

Reineildo/Lenglet/Gimenez/Llorente

well, the key strategic factors for atleti is conversion rate + percentage of intercepted passes.... the totally unimportant factors are quantity of strikes or possession

The game begins and a cool,

it starts with poor defense from a real madrid player, somehow a player outmuscled a player bigger than him, then Guiliano gets to the ball first, and released Alvarez, alvarez released depaul, depaul crossd, and the ball was dummied and gallagher made th secondary run. the goal started with poor defense, not pressure from atltico madird

7:40 Llorente terrible defense on vini there

8:35 so far, atleti have a high conversion rate 100% and have not lost a pass, these are the things atleti need to do, pressing is bullshit, not every strategy is a mirror of barca

11:30

exactly alvarez, dont let real madrid have that low switch

13:13 a foul tht would had led to a penalty just happened middle of the park

14:26 interesting, bellingham love guiliano simeone, i can comprehend why, jude does a lot of work for real madrid covering for mbappe's selfishness aka cr7 ways

19:32

the key is goal conversion rate+ percent of their own passes intercepted , so far atleti is doing well, high in goal conversion low in their own passes intercepted.. ahh don't force it guiliano, we don't have the speed

28:19

Atletico madrid squad can not run with real madrid or fc barcelona, or psg, atletico madrid this season play an open system, with an athletically normal squad, it is a reactive system . the key is passing completion percentage why? because the goal is to pass through the sectors , play one twos, atleti can not recover from a real madrid counterattack .... squads quality determines the system a coach can play , not the coaches desires

31:29

and you and jorge just proved why you both should only speak when barca is playing because you both don't know the game. if you can't comprehend how to win with all styles against all styles then you don't know the game

37:03

I don't believe any team can do anything, I am not a predictions fan, that is you jorge, steeve and others, all of you are in the predictions game, whatever happens will happen, each team tries to perform a strategy, on assessment you can see what worked or not, but all strategies can win and all strategies can lose against each other. it is game by game for me. All I expect is for my teams to try to win and they always do, I have no idea what belief has to do with anything , that is fanaticos like yourself

37:30 the ref called a foul on a msidribble by mbappe depaul didn't foul him. and then no card on tchouameni for a trip

Atletico madrid by 38:58 have mostly hit the target on attempts. I saw three misses, three too many but the interception of atletico madrid passes is still low, i only see three by now, that is very good, atleti play expansive + reactive, so giving the pass away is bad.

41:50 bellingham + tchouamnei not talking to each other, basics, again, why arent' they talkin to each other

42:56 Barrios pulled shirt , well simeone trust the rotation, barrios has to comprehend, the atleti system isn't lazy, meaning the press system that is beloved in the spanish flag team or barca allows for defensive ignorance, simeone wants a team that does everything greatly, attack/press/possess/defend absent the ball well!

halftime

i am saying a run and gun can't win , it doesn't matter who, oddly enough, a number of run and gun teams are in the tournament which gives the gambling odds a run and gun team will win. Arsenal/Barca/PSG are all the same, press/attack no defense through possession + no ability to defend absent the ball. Can they win matches of course, but in most cup torunaments they face a team that can do the strategic solution, can defend absent the ball very well + has a high conversion rate+ can counterattack using low quantity of aerial balls which requires attentive players

54:!7 guiliano you have to control that, that is a bad giveaway, atleti's system requires passing accuracy to be very high

59:10 real madrid having a problem making the switch above the low block phase, luckily real madrid have great athletes all about the pitch

59:48 ahhh, lenglet and Gimenez both have been very poor in their conversion today costly, atleti need high conversion, meaning attempts need to lead to goals or saves, they both had two headers won and didn't hit the target

65:30

modric/someone else out vasquez/camavinga in

69:14 i see, valverde was taken out, you see this is why the press can't work for atleti, we don't have the speed to catch teams

Giuliano, love his heart, but now maybe all of you barca fans will see, not all teams can play the press attack, you need players who have the speed to do that, atleti don't, atleti play a passing system, it fits the squad we have, we don't have any explosive dribblers or speedsters. llorente + guilani are positional players

Reinildo, the art of defense, lovely tackle, read rodrygo the whole way

77:10 Gallagher is having his best game all season, i have to say that, he has never been in as good position, timed tackles so well, played so well forward all season ... the set pieces of atleti have been poor this game, we have good takers but been poor, atleti have a problem against tall teams, we need to keep the ball we can't pass frenetic

no stay gallagher this is the best al season from you, gallagher out for Lino 84:54

85:45 Griezzman + Lino some great passess real madrid aren't pressing, now atleti can compress with out open play

87:01 everyone take a look, that wasn't a foul , real madrid have stopped running collectively, Lino great work defensively

88:21

Guiliano/ griezzman

Sorloth /Correa

the beast is coming in now for griezzman, and real madrid have collectively stopped running, no press

if you would had scored correa! ohhh

he did everything right

ahh atleti, we have done great with the passing which is what the atleti system demands, but the conversion rate has gone down ahhh Depaul is out, hamstring aww no

2:26 depaul is out, Guiliano simeone/griezzman/gallagher/depaul all had great games, we look like we will win in normal time, Molina it is time,

the problem is, girezzzman/depaul/are our best passers, extra time ahhhh

92:41

correa what a throw from oblak and a run by correa, sorloth is too slow to outmanuever, rudiger, have to go high correa

bellingham just said fuck off, shouldn't that be another yellow:) 93:50 nice win sorloth, good work , keep fighting

97:34

reinildo looks out, and now azpilicueta is coming in:) hahaha this is great:) oh atleti, look at this squad:)

98:00 no sorloth, that was it, Barriso gave him a great pass, no!!! the conversion rate, i said it altetico madrid is at our best when we have over 95% no intercepted passes and we have a high conversion rate, the conversion rate of atleti is too low now, that was the game sorloth comeon BEAST!

101:40 ahhh atleti, Lino was on, why the pass so hard , atleti is tired, the execution is lessened.

second half of extra time

circa 106th minute

the bestchance of extra time is the barrios to sorloth , everyone try to find it, you will see, the beast had to score that, i argue that was the best chance of the game

109:58

look at the athleticism o real madrid, magic, can out run anybody

115:19

uh oh, the young beast, endrick in for vinicisujr, maybe

117:34

in defense of llorente, that is a lat etackle

EDN OF REGULAR TIME

penalties, tell me folks i am done, great game atleti, had our chances, again, got to be more clinical, lovely game

#rmsoccer

[neuromycelic-blog]

The figure of Li Hong, as a Taoist messianic symbol of cosmic renewal and justice, offers **metaphorical and ideological resonance** for contemporary movements seeking systemic change. While his myth is rooted in ancient Chinese cosmology and sociopolitical contexts, his symbolism can inspire modern critiques of inequality, corruption, and ecological collapse. Below are ways Li Hong’s themes intersect with current revolutionary needs:

---

### **1. Challenging Corrupt Systems**

Li Hong’s return was prophesied to dismantle oppressive regimes and restore harmony (*Taiping*). Today, his myth parallels global movements opposing **authoritarianism, corporate greed, and environmental exploitation**. The idea of a "cosmic reckoning" resonates with calls to dismantle systems that prioritize profit over people and the planet.

- **Example**: Climate activists like Greta Thunberg frame ecological collapse as a moral failure of governance, echoing Li Hong’s role as a divine corrector of imbalance.

---

### **2. Collective Action and Hope**

Li Hong’s followers believed collective faith and ritual could hasten his arrival. Similarly, modern revolutions depend on **mass mobilization and shared vision**. His myth underscores the power of hope in sustaining movements during crises.

- **Example**: The 2019–2020 Hong Kong protests invoked shared ideals of justice, much like Li Hong’s devotees rallied around *Taiping*.

---

### **3. Spiritual Renewal in Material Struggles**

Li Hong’s promise of *Taiping* fused spiritual and material liberation. Today, many activists stress the need to address **spiritual alienation** (e.g., burnout, nihilism) alongside material inequities. Taoist concepts like *wuwei* (non-coercive action) and balance could inform holistic approaches to revolution.

- **Scholar Terry Kleeman** notes that Celestial Masters rebellions blended ritual and politics, suggesting revolutions thrive when they nourish both body and soul (Kleeman 2016, 107).

---

### **4. Cyclical Cosmology vs. Linear Progress**

Li Hong’s myth reflects Taoism’s **cyclical view of history**, where collapse precedes renewal. This contrasts with Western notions of linear progress but aligns with Indigenous and ecological critiques of unsustainable growth.

- **Relevance**: Movements like *degrowth* and Indigenous land-back campaigns reject infinite capitalist expansion, embracing cyclical renewal instead.

---

### **5. Caution Against Co-optation**

Historically, rulers like the Tang dynasty co-opted Li Hong’s symbolism to legitimize their power. Similarly, modern revolutions risk being hijacked by **authoritarian leaders** or diluted by performative reforms.

- **Lesson**: True revolution requires vigilance against empty symbolism and centralized control.

---

### **6. Utopian Vision**

Li Hong’s *Taiping* was not just rebellion but a blueprint for a harmonious society. Modern movements often lack clear visions of post-revolutionary worlds, leading to disillusionment.

- **Inspiration**: The Green New Deal and mutual-aid networks attempt to prefigure utopian ideals, much like Taoist communities modeled *Taiping* through egalitarian practices.

---

### **7. Cultural Reimagining**

Li Hong’s myth was adaptable, absorbing Buddhist and local influences. Today, successful revolutions must **transcend cultural boundaries**, integrating diverse voices (e.g., BLM’s global reach).

---

### **Limitations and Risks**

- **Messianic Leadership**: Li Hong’s top-down "savior" model conflicts with modern emphasis on decentralized, grassroots leadership.

- **Escapism**: Overemphasis on cosmic renewal risks diverting energy from tangible organizing.

---

### **Conclusion**

Li Hong’s relevance lies not in literal emulation but in **symbolic inspiration**: the need to root revolution in hope, holistic justice, and a vision of balance. As scholar Isabelle Robinet writes, Taoist messianism "responds to despair with the promise of a world reborn" (Robinet 1997, 83). In an age of polycrisis, this ethos urges us to reimagine revolution as both protest and prophecy—a fusion of immediate action and transcendent purpose.

---

**References**

- Kleeman, Terry. 2016. *Celestial Masters: History and Ritual in Early Daoist Communities*.

- Robinet, Isabelle. 1997. *Taoism: Growth of a Religion*.

[studiestoday123]

Explore comprehensive resources for CBSE NCERT Class 11 Maths Linear Inequalities on StudiesToday. Access detailed notes, solved examples, and practice questions to master linear inequalities and excel in your exams. Enhance your understanding and boost your confidence.

[math-journal]

Here — Algebra 2

Elementary Algebra

Unit 10

Fraction/Decimal Busters

Special Case Equations

6 Step Application Question

Inequalities

Solving Compound Inequalities

Solving Absolute Values

Application Problem Steps

Notes

~Silly Wizard Review~

Unit 11

Property of Exponents

Scientific Notation

Combining Like Terms

Multiplying and Dividing Polynomials

Degrees of Polynomial

Unit 11 review

Unit 12

Factoring Polynomials

Difference & Sum of Squares

Factoring Trinomials

Application Problems

Unit 13

Graphing Linear Equations [1]

Find x- and y-intercept

Graphing Linear Equations [2]

Finding Slope

Parallel and Perpendicular

Solution Strategies

ll & +

Graphing Inequalities

Unit 14

Systems of Equations

^ Examples

Substition & Elimination Ex

Application Problems

Review

—> Next

[852-between-the-pages]

"Moth Smoke" by Mohsin Hamid – An Incisive Social Commentary.

Rating: ★★★☆☆ (3/5)

"Moth Smoke" by Mohsin Hamid is a compelling and thought-provoking novel that delves into the complexities of class, love, and self-destruction in modern-day Pakistan. With its richly drawn characters, evocative setting, and incisive social commentary, Hamid's debut novel captivates readers from the very first page.

One of the novel's strengths lies in Hamid's vivid and atmospheric portrayal of Lahore. Through his prose, the city comes alive, with its bustling streets, vibrant markets, and stark class divisions. Hamid skillfully captures the essence of Pakistan's socio-political landscape, providing readers with a glimpse into the complexities of a rapidly changing society.

Hamid's characters are complex and flawed, adding depth and authenticity to the narrative. Darashikoh, in particular, is a deeply conflicted protagonist, torn between his desires, societal expectations, and a growing sense of disillusionment. Hamid's exploration of class dynamics and the stark disparities between the privileged and the marginalized is both astute and unflinching.

"Moth Smoke" is not just a story of personal struggle; it is also a scathing critique of a society grappling with corruption, inequality, and the consequences of rapid modernization. Hamid artfully weaves in themes of power, justice, and the consequences of one's actions, highlighting the moral ambiguities that permeate the lives of his characters.

The narrative structure of the novel is inventive and adds an extra layer of intrigue. Through alternating perspectives and non-linear storytelling, Hamid keeps readers engaged, slowly revealing the interconnectedness of the characters' lives and the consequences of their choices. This narrative approach mirrors the fragmented nature of the characters' lives and adds depth to their development.

Hamid's prose is sharp, intelligent, and infused with dark humor. His writing style is both accessible and literary, allowing readers to immerse themselves in the story while reflecting on the deeper themes and social commentary. His ability to evoke emotions and create a palpable sense of tension is impressive, making "Moth Smoke" a compelling and engrossing read.

However, it is important to note that "Moth Smoke" can be a challenging read at times. The novel tackles complex themes and does not shy away from depicting the darker aspects of human nature. The characters' flaws and their actions may be unsettling for some readers. Nevertheless, it is through these uncomfortable moments that Hamid shines a light on the complexities of power, desire, and the consequences of societal pressures.

In "Moth Smoke," Mohsin Hamid showcases his talent as a writer and storyteller. Through his exploration of class, desire, and moral ambiguity, he presents a nuanced and thought-provoking narrative that lingers in the reader's mind long after the final page. Fans of literary fiction and those interested in gaining insights into contemporary Pakistan will find "Moth Smoke" a compelling and rewarding read, showcasing Hamid's ability to illuminate the human condition within a complex societal framework.

Asia Rahman Khan Lodhi [Consul Press at the Consulate General of Pakistan, Hong Kong (SAR) & Macau (SAR)]

Note: This review is based on the original publication of "Moth Smoke" and not any subsequent editions or adaptations. The views/ ideas in the book are purely of the book’s author and are not necessarily endorsed by the book reviewer. 

[jniejadlik]

An analysis of video infographic Wealth Inequality in America

Wealth Inequality in America uploaded by Politizane ten years ago incorporates a variety of visual approaches in explaining how wealth is distributed in the United States. With such a numbers-heavy topic, if only writing about wealth inequality, a reader may lose interest and/or become confused. With a video infographic, the same topic of wealth inequality comes to life. By telling the story through six and a half minutes of color, movement, charts, graphs and narrative, the audience finds that the ideas of wealth inequality when compared to the realities of wealth inequality are not one and the same.  

            The video opens with the words “Wealth Inequality in America” in patriotic red, white and blue colors. A voice narrates while moving and changing visuals catch the eye. An outline map of the United States of America appears and then is replaced with images of one-hundred-dollar bills.  Right from minute one, a semiotic visual approach is detected. Symbolic colors are used purposefully so the audience immediately ties those colors to the U.S. map. Viewers are cued to know this is about America. And about money. Next, iconic symbols, one-hundred-dollar bills, fill the screen. Money in the United States and how it is shared or not shared is going to be explained. Through the use of symbols, this video creates a metonymic code “causing viewers to make assumptions about what is being viewed” (Lester, 2020, p. 66).

From a constructivist perspective, this video offers many pieces to pull together the intended message. Initially a bar chart is presented and divided up by various color sections showing what people think wealth divisions are across all groups in America. Then it shifts to show what the divisions actually are. To help reframe this wealth division, the video shifts to show a linear breakdown of only 100 people, representative of the entire population, to offer a visual that feels more manageable.

All of these pieces and elements allow the viewer to take each part and construct an understanding about what is happening with wealth in this country. A bit later in the video, a pie chart, along with an image of a clock and a calendar are presented to further illustrate salary discrepancies. As a viewer, we are taking all these bits to create an understanding of how wealth is distributed and furthermore what this means for a typical worker.

From a gestalt visual approach, this video offers a simple way to grasp existing wealth differences and inequalities. Groups are separated by wealth category. Although the initial divisions are broad and simply color coded, a shift to the use of a visual of people lining up and moving and re-grouping according to their part of the wealth spectrum shows a viewer “a steady row of folks based on their net worth” (Politizane). This video also repeatedly shows a smooth continuation of perceived movement, which Lester (2020) notes is something the brain seeks as much as possible (p. 53).  While initially presented in a similar gray color, the groupings change color so they are grouped together on the wealth band. The differential in wealth is especially evident when the 1% group is separated from the remainder of the population and the viewer not only sees but hears “1% of Americans have 40% of all the nation’s wealth (Politizane).”

This video is visually appealing, vibrant, and offers up data in a way that feels manageable. It is not surprising, from a cognitive design perspective, why this is a popular video. It is memorable for a variety of reasons. Charts appear, images flash, and it is easy to become distracted and caught up by all the financial figures being presented. Audiences, coming from a cognitive visual theory perspective, should remain mindful regarding who is producing content and why. Each viewer will perceive this message differently and especially when abstract concepts like “fair” and “equitable” are mentioned, it can be assumed that each viewer will perceive concepts differently. Depending on a viewer, one may consider this work as persuasion while another may see propaganda. If a creator remains anonymous, it can be valuable to question why. When content seemingly focuses on dividing people, but offers no solutions to fix the issue being presented, it may be valuable to do additional research as opposed to just getting caught up in viral content. Fortunately, a references screen is provided at the end of this video, offering the viewer a starting point in researching this topic themselves.

Sources

Lester, Paul Martin. (2020) Visual communication: Images with messages (8th ed.). Dallas: Lex Publishing.

Wealth Inequality in America by Politizane retrieved on May 30, 2023 from

[er-cryptid]

Graphing Linear Inequalities

-- for the vertical line x = a      -- if x > a, shade the half-plane to the right of x = a      -- if x < a, shade the half-plane to the left of x = a

-- for the horizontal line y = b      -- if y > b, shade the half-plane above y = b      -- if y < b, shade the half-plane below y = b

.

Patreon | Ko-fi  

[neet-aspirant]

29–11–2023, Wednesday

je mange un gâteau (I'm acing french omg). here's the hello kitty mug I'd talked about. also, i'm going to school tomorrow (and hopefully the rest of the week) so #studyspo might not be too often. i'll make sure to update though, even if my days aren't too productive because of my insane school hours.

learnt a portion of my psychology chapter

solved linear inequalities for an hour

reviewed notes for my chem practical exam

attended a 2 hour chem lecture

2 hours of French on Duolingo

reviewed photosynthesis notes for an exam on sunday

[studydork]

🌼8/???

So!

☑ Classes done! They were so fun too, my boys were being so active today, really proud of them and glad to work with the kids who participate in lessons.

☑ French vocabulary lesson also done, I got to write down words for colors, revise numbers and learn new verbs.

☑ Did SAT math studying, started with heart of algebra because I don't trust myself with my math knowledge-😂 Spent an hour looking at linear equasions and inequalities trying to make sense of it all.

☑ Drew little meme gift for my friend. It's fun to know that none of my friends I actually talk with for years because of Tumblr in the first place know I have this studyblr now.

☑ Spent time to write an outline for a few scenes in a fanfiction I'm writing.

Satisfied with today and ready for the next days to come 😌

Plans for tomorrow:

• Clean the house

• Church group

• Revise French flashcards

• Finish notes for chemistry

[arcticdementor]

The University of California system is getting rid of its SAT/ACT requirement. More will follow.

There’s a lot to say. First, we must distinguish between two types of tests, or really two types of testing. When people say “standardized tests,” they think of the SAT, but they also think of state-mandated exams (usually bought, at great taxpayer expense, from Pearson and other for-profit companies) that are designed to serve as assessments of public K-12 schools, of aggregates and averages of students. The SAT, ACT, GRE, GMAT, LSAT, MCAT, and similar tests are oriented towards individual ability or aptitude; they exist to show prerequisite skills to admissions officers. (And, in one of the most essential purposes of college admissions, to employers, who are restricted in the types of testing they can perform thanks to Griggs v Duke Power Co.) Sure, sometimes researchers will use SAT data to reflect on, for example, the fact that there’s no underlying educational justification for higher graduation rates1, but SATs are really about the individual. State K-12 testing is about cities and districts, and exists to provide (typically dubious) justification for changes to education policy2. SATs and similar help admissions officers sort students for spots in undergraduate and graduate programs. This post is about those predictive entrance tests like the SAT.

Liberals repeat several types of myths about the SAT/ACT with such utter confidence and repetition that they’ve become a kind of holy writ. But myths they are.

1. SATs/ACTs don’t predict college success. They do, indeed. This one is clung to so desperately by liberals that you’d think there was some sort of compelling empirical basis to believe this. There isn’t. There never has been. They’re making it up. They want it to be true, and so they believe it to be true.

…

2. The SATs only tell you how well a student takes the SAT. This is perhaps a corollary to 1., and is equally wrong. They tell us what they were designed to tell us: how well students are likely to perform in college. But the SATs tell us about much more than college success. Let me run this graphic again.

…

3. SATs just replicate the income distribution. No. Again, asserted with utter confidence by liberals despite overwhelming evidence that this is not true. I believe that this research represents the largest publicly-available sample of SAT scores and income information, with an n of almost 150,000, and the observed correlation between family income and SAT score is .25. This is not nothing. It is a meaningful predictor. But it means that the large majority of the variance in SAT scores is not explainable by income information. A correlation of .25 means that there are vast numbers of lower-income students outperforming higher-income students. Other analyses find similar correlations. If SAT critics wanted to say that “there is a relatively small but meaningful correlation between family income and SAT scores and we should talk about that,” fair game. But that’s not how they talk. The routinely make far stronger claims than that in an effort to dismiss these tests all together, such as here by Yale’s Paul Bloom. (Whose work I generally like.) It’s just not that hard to correlate two variables together, guys. I don’t know why you wouldn’t ever ask yourselves “is this thing I constantly assert as absolute fact actually true?” Well, maybe I do.

In general, progressive and left types routinely overstate the power of the relationship between family wealth and academic performance on all manner of educational outcomes. The political logic is obvious: if you generally want to redistribute money (as I do) then the claim that educational problems are really economic problems provides ammo for your position. But the fact that there is a generic socioeconomic effect does not mean that giving people money will improve their educational outcomes very much, particularly if richer people are actually mildly but consistently better at school than poorer for sorting reasons that are not the direct product of differences in income. That is, what correlation does exist between SES and academic indicators might simply be the metrics accurately measuring the constructs they were designed to measure.

And throwing money at our educational problems, while noble in intent, hasn’t worked. (People react violently to this, but for example poorer and Blacker public schools receive significantly higher per-pupil funding than richer and whiter schools, which should not be a surprise given that the policy apparatus has been shoveling money at the racial performance gap for 40 years.) All manner of major interventions in student socioeconomic status, including adoption into dramatically different home and family conditions, have failed to produce the benefits you’d expect if academic outcomes were a simple function of money. I believe in redistribution as a way to ameliorate the consequences of poor academic performance. There is no reason to think that redistribution will ameliorate poor academic performance itself.

5. SATs are easily gamed with expensive tutoring. They are not. This one is perhaps less empirically certain than the prior two and on which I’m most amenable to counterargument, but the preponderance of the evidence seems clear to me in saying that the benefits of tutoring/coaching for these tests are vastly overstated. Again, a simplistic proffered explanation for a troublesome set of facts that then implies simplistic solutions that would not work.

6. Going test optional increases racial diversity. This one, I think, must be called scientifically unsettled. However both Sweitzer, Blalock, and Sharma and Belasco, Rosinger, and Hearn find no appreciable increase in racial diversity after universities go test-optional. “Holistic” application criteria like admissions essays almost certainly benefit richer students anyway. What’s more, we have to ask ourselves what “diversity” really means in this context. Private colleges and universities keep the relevant data close to the vest, for obvious reasons, but it’s widely believed that many elite schools satisfy their internal diversity goals for Black students by aggressively pursuing wealthy Kenyan and Nigerian international students, whose parents have the means to be the kind of reliable donors that such schools rely on so heavily. I’m not aware of a really comprehensive study that examines this issue, and it would be hard to pull off, but the relevant question is “do various policies intended to improve diversity on campus actually increase the enrollment of American-born descendants of African slaves?” I can’t say, but you can guess where my suspicions lie.

…

All of that is prologue to the bigger point: the controversy over college entrance examinations stems not from the examinations themselves, but from the fact that they reveal profound differences in human capital that make progressives uncomfortable. The SATs don’t create inequality. They reveal inequality.

…

The racial achievement/performance gap is a curious thing even in the context of an American political discourse that seems to get more bizarre by the day. That the gap exists is, on balance, not controversial. Gaps in performance are observed on essentially every measured academic metric, though the size of the effects vary from context to context, and the general distribution is Asian American students at the top, white students next, then Hispanic, then Black. The Black-white gap in particular has shrunk from the era of (explicitly) segregated schools but progress has not been consistent or linear. Most people in academia and politics admit it exists: prominent Black politicians like Barack Obama and Kamala Harris reference it, every major think tank and foundation operating in the educational space identifies it as a major priority, and the NAACP used to address if often, though their Education and Education Strategy pages have recently disappeared so it’s hard to know where they stand now. These things are faddish but once upon a time every other dissertation written by someone getting a PhD in Education was about the gap. We can observe it even outside of reference to controversial tests, such as noting that the white high school graduation rate is 10% higher than that for Black students. The achievement gap is a thing.

And yet I also find a rapidly-congealing social prohibition against talking about these gaps in progressive spaces. If you refer to a racial achievement gap in a lot of liberal or left contexts now, you’ll find that people clam up fast and get visibly uncomfortable, even if you take pains to point out that an academic achievement gap does not imply an academic potential gap. People just don’t want to acknowledge that gaps exist at all; our racial discourse appears to have become such a blunt instrument that the acknowledgement of racial difference is controversial even when you preface discussion with the belief (that I hold) that the gap is the product of innumerable environmental and sociocultural factors rather than genetics or other inherent differences. Simply saying “Black students consistently score lower on tests like the SATs, have lower average GPAs, and have worse metrics on ancillary concerns like truancy” - again, Barack Obama’s position, Kamala Harris’s position, Cory Booker’s position - is enough for people to start launching into harangues about the inherent violence of those comparisons. People just do not want to talk about this stuff.

…

Those concerns with group differences, at least, have some sort of basic political logic and are amenable to complaints that they are the product of systemic inequality. (They are, but not the inequalities that people think, and again the SAT gap is a result of systemic inequality, not a cause of systemic inequality.) More disturbing to me is the rise of resistance within academia to the notion of inequalities between individuals. When I was in grad school more than a half-decade ago, I observed with some considerable unhappiness that it had become increasingly socially unacceptable to speak of some students as simply better students than others, as being more talented, harder working, or more prepared. All of this was seen as inegalitarian and, eventually, as “white supremacist” even if every student being compared in a given context was white. There were many instructors back then who bragged about giving all students As, etc., and I must assume this practice has only grown over time. In the humanities and social sciences especially there is a growing movement to reject assessment, including grading - the means through which we sort better students from worse - as the hand of illegitimate power that “does violence” to the students who voluntarily attend college.

…

Of course, that complicity in the neoliberal machine is not some recent injustice; it is the very reason that colleges and universities are funded by our society at all. If this trend continues, not just eliminating SAT requirements or increasingly refusing to hierarchize students with grades but in rejecting the entire sorting function of the university, academia will collapse. Wealthy parents aren’t paying Harvard to enrich their children in the humanistic sense. They’re paying Harvard to act as a marker of their child’s superiority in the labor market and the social hierarchy. Employers value college because it provides at least some meaningful information about who will succeed as a worker; remove that function and the financial justification for a hideously expensive system dies. I would love if education dropped its association with meritocracy, but that cannot occur within our current system. The professors who self-aggrandize through their rejection of their hierarchizing function, if successful, would cause the doom of the modern university. (These tenured radicals, of course, never are so moved by the inherent inequities of academia that they quit the profession.)

Today, it is somehow controversial to say “some people are smarter than others,” a reflection of one of the simple brute realities of human life and something that has been accepted as true for thousands of years.

Here is the essence of it: hierarchies of relative academic performance are remarkably stable throughout life, due to differences in inherent or intrinsic academic ability of whatever origin, and the SATs and similar mechanisms reveal those differences in a way that liberal America is increasingly unable to accept. This is the source of all of this angst, not the technical details of whether a test is fair or valid or just, but a liberal intelligentsia that is incapable of honestly confronting the fact that different human beings have fundamentally different intrinsic abilities. I believe in political equality, social equality, equality of rights, equality of dignity, equality of protection under the law. But the notion that all people are equally talented, in academics or anything else, is an absurdity, and as much as people will rush to deny intrinsic difference, I suspect that pretty much everybody knows that they are real. When you were a child you casually assumed that some of your classmates were naturally better at school than others, and you did because it was true.

This is the conversation that I tried, and failed, to force with my book: left-of-center political movements, from center-left to radically socialist, cannot achieve the goal of the greater good for everyone, including greater political and economic equality, while pretending that we believe in equality of human ability. The only way to intelligently address various social, economic, and political equalities related to differences in human potential is to acknowledge that those differences exist. The current rending of garments regarding inequalities within our education system has led to certifiably bizarre situations like the movement, currently gathering steam, to teach math as if it is as subjective as literature or art. But this won’t make Black kids or poor kids or girls or anyone else actually better at math. And if the universities really give up their function of creating an academic hierarchy for political reasons, employers will find new systems that do that, or a lot of people will get hired and quickly fired for not being competent. This is not an intelligent policy approach. Getting rid of the SATs won’t make unprepared kids prepared. It won’t make naturally untalented students naturally talented. It won’t make kids who aren’t smart into smart kids. All it will do is hide the reality of those unpleasant inequalities.