#math class

[one-time-i-dreamt]

Someone passed me a note in my math class and when I opened it it was a drawing of a hare. The hare looked at me and said, “The mountains have roots. They want the sky back.” And then the ink seeped through the paper until I was holding a completely black and soaked note.

[thedungeonbat]

calculus :)

managed to work for ~2.5h despite feeling quite tired and having a headache (I need a coffee alternative as I simply can’t stand the taste anymore…)

[randomuniversityquotes]

Differential Equations Professor: "...so this is like, super easy."

[schoolchaos]

Is it weird that math is my second favorite subject (art is my first favorite) despite being absolute shit at it?

Like, I will be failing every quiz/test we ever have for math but also I will 100% willingly do the homework

Can I add 5 to 6 in my head? Fuck no. Will I love trying to solve for x? Yes, definitely.

[devorafetos]

The bad part of becoming so fixated on dead people (and invested in my own fic) is that when I remember and truly seize the fact that John Laurens died at 27, so young and full of potential, in love and with so many possibilities, I break down crying in some of the most random places

[coolballoonsheep]

I was so bored in math class😭

[junkracco0n]

i hate when hoes beg me for gum. NO IM NOT GONNA GIVE U A PIECE. IDK WHO U ARE

[alexiaa049]

I made this little doodle of the doctor in math class because I was bored

[melloyello-69]

Mello school doodles :D

[rayisnthere14]

How I feel in math class when something actually clicks in my head 😭

Also fun fact! I actually need glasses irl- I had some for like a year and then just.. Stopped using them 💀

[thedungeonbat]

~5 hours of math later & im exhausted

Mock exams, again. This time the whole bundle of ones from 2020. Math class was cancelled today, our homework was to continue studying on our own so that��s what I did :‘) it was exhausting but also fun- tho I am getting tired of doing calculus lol I’ve reached the point of not being able to think straight so I’ll call it a night and leave studying for tomorrow.

[randomuniversityquotes]

Differential Equations Professor: "I have a matrix here, and a number here. That's a crime."

[cams-math-rants]

Finite and Infinite Sets

Recently, in my Discrete Mathematics course, we have been discussing the title of this blog post. It took me some time to understand these concepts, but it is finally clicking in my mind and it’s all I can think about at the moment.

First, I’d like to discuss some definitions.

When I mention the notion of a set, this refers to a collection of objects/numbers (we call each number in a set an “element”) in which the order doesn’t matter (unlike with sequences). An example of a set is ℝ, the set of all real numbers. Another example that will become important later is ℕ, the set of natural numbers (positive integers starting at 1).

A bijection refers to when every element in one set maps onto a unique element in the other set. When we map a set onto another, we write X → Y. This is shown in the image below, because it helps to see this visually.

When two sets are equinumerous (written X ≈ Y for two sets X and Y), this simply means there is a bijection between these sets.

By definition, in order for a bijection to be possible, the two sets have to contain the same amount of elements, or have the same cardinality (written |X| = |Y|, which in English means “the cardinality of X equals the cardinality of Y”). This means the two sets have the same size.

Now, we can talk about finite and infinite sets. The notion of a finite set is rather intuitive: there are n elements in a set X where |X| = n. An infinite set also makes sense conceptually, where the elements never reach a boundary. However, there are different kinds of finite and infinite sets that makes things interesting.

We can say a set is denumerable, which means we get a bijection when mapping ℕ to said set. An example of this is the set of integers, ℤ. When we have ℕ → ℤ. We can show this by representing this as a piecewise function and separating the integers into even and odd, and we find that there is a one-to-one, unique correspondence between the two sets (perhaps I will go through this proof in another post but there are examples online).

A denumerable set can be infinite or finite. In the example above, ℤ is infinite and denumerable. When a set is countable, that means a set is either finite or denumerable.

What is interesting is when we have an infinite and uncountable set, such as ℝ. In this case, there is a beautiful way to prove such a thing using Cantor’s Diagonal Argument. I won’t discuss this in full here, but here is the link to the Wikipedia article: https://en.wikipedia.org/wiki/Cantor's_diagonal_argument?wprov=sfti1

Thanks to anyone who has read my post. My name is Cameron and I’m a math major that loves to discuss what I’m learning in my classes. Keep in mind that I am not an expert, so I am open to anyone scrutinizing my explanations if you believe something is represented wrongly.

This is the song I’m currently listening to on repeat:

[sageisntamathperson]

Math people of Tumblr: what books should I read/YouTube should I watch to “get into” math beyond what they teach in school? I’m in Algebra 2/Precalc, if that helps :)

[nataitalynaty]

"Math?"

Caine, it's not mathematics my darling... it's analytical geometry 🤭🔫