#Finite and Infinite

[tonreihe]

“God stands on the far side of our notions of finite and infinite.”

—Hans Urs von Balthasar, The Theology of Karl Barth

[turiyatitta]

The Enigma of Nine

A Metaphysical Exploration into the Significance of a Singular Number In the vast expanse of numbers and their mathematical precision, there lies a mystical depth, a metaphysical dimension that transcends their apparent functionality and dives into realms of deeper significance. During our conversation with Steve James on Guru Viking, I ventured into the enigmatic world of the number nine,…

[nb-hedgewolf]

9-Finite AU

Time is not chronologically consistent when it comes to the rifts the phantom ruby may tear between two worlds, two objects entering the same crack will end up separated by almost a year when they arrive to the other end. This time aberration may cause that from the perspective of someone in one end, time moves extremely fast or extremely slowly in the other end. While Classic Sonic might spend a short amount of time on the Modern world, for the Classic world... it's been years under the control of Robotnik. It shouldn't be a surprise for either blue hedgehog to find out Eggman's newest bioweapon is none other than their sibling, turned bitter by a horrible world, without the guidance of his brother.

[starry-bi-sky]

"Odysseus and his crew could've just fished!"

"lmao Athena is yelling at Odysseus for not fishing instead"

"why didn't they just fish? they're on the ocean!"

Me, tiredly: no.... no they could not have 'just fished', you don't know what you're talking about. please... please just sit down. Athena would've "my goodbye"'d his ass on the spot for suggesting to fish instead

[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:

[spoofaloofa]

I love the Thunderhead so much you guys have no idea I NEED TO CONDUCT EXPERIMENTS ON THIS THING. ITS SO FASCINATING TO ME. “I would be heartbroken if I had a heart capable of breaking.” Okay. Nods and scribbles faster on my clipboard. Thunderhead I am diagnosing you with Shepherd’s Guilt. Heres a sticker and a lollipop. Go have fun or whatever

[stoicmike]

Truth is finite -- bullshit is infinite. -- Michael Lipsey

[desire-mona]

i cant stop being sad about the lack of space travel in 17776, i just cant. i know we tried our best, and i know we spent years and years and years making the most advanced spacecraft we could with the materials we had on earth. i know. but i also know that one day, no matter how many millions or trillions of years in the future, we will grow bored of earth.

im not saying itll happen anywhere even remotely close to soon, but one day the football wont be enough anymore. we move onto other sports, bending and editing the rules to make as convoluted game possible, playing them all for thousands upon thousands of years, and eventually grow bored. we bend the rules for as many fun activities or games as we can, make entirely new games, invent unthought of ways to entertain ourselves, but eventually itll all get boring. humans are, in all possible accounted for ways, entirely immortal, theyre going to live FOREVER. no matter what. theres a lot to try, do, and get bored of when you have until the end of time itself, which is all well and good until you realise that the earth is finite, no matter how large it is.

we'll run out of shit to do eventually, simply because there isnt enough of anything to last forever. you cannot be entertained for the rest of your infinite life on a finite planet.

[saphushia]

so is etho's body completely hollow inside? or are there organs or other stuff just Floating Around in there

Hmmm so yknow when you're playing minecraft and a chunk hasn't loaded yet. And technically, that unloaded chunk isn't really empty, the data is all there, you just can't see or interact with it.

Like, he can still see out of his 'missing' eye (tho its a lil fuzzy), but you can't touch it or even see it in any way. So his other organs work on similar logic. He still bleeds when you cut him and gets by just fine Organ function wise, it just so happens a significant portion of his organs don't exist tangibly.

So basically he has holes all over his body that lead to void filled pockets, but at the same time he has perfectly average and normal human physiology. Both exist at once

[ian-the-existential-crisis]

I really want to write a story where one vampire offers to turn their lover under that romantic bullshit of true love and destiny and they end up breaking up after like 10 years. Then 1000 years down the line they both accidentally bump into each other in fucking Manhattan and one of the vampire is a raging lesbian and the other one is an asexal femboy and it took hundreds upon hundreds of years apart to realize that they were meant to be good friends for all eternity, not lovers.

[justalittlebluetiefling]

That was such a good conversation. Emhira is obviously the perfect one to have that moment with. And it was GOOD.

[shrinkrants]

An informative and useful overview of how an infinite, rather than a finite, approach to organizing is what's needed in today's struggle. Well worth the time it takes to read.

I really admire Scot Nakagawa's ability to condense and describe what's involved in anti-authoritarian organizing.

[kiragecko]

Gecko: I need to read all these comics so I can get an accurate idea of the characters and how they changed over time

Also Gecko, after reading issues that showcase a change they don't like: this is AHISTORICAL BULLSHIT, and I'm going to cherrypick fill-in issues that still use the old characterization for my data!

[timehascomeagain]

if see no end in is by frank bidart

[foundationsofdecay]

when’s st gonna do smth like this for the new era, idc if it’s w the espera group or as a shoot representing him and sleep, i need it in my life

[obstinaterixatrix]

I would also love for people to understand that. you don't have to tell on yourself.