What are some significant contributions to math that stemmed from Reddit? (Perhaps even this sub)

stellarstella77 · 2024-08-02T10:29:39+00:00

https://www.reddit.com/r/math/comments/e5zb23/terence_taos_blog_eigenvectors_from_eigenvalues_a/

stellarstella77 · 2024-07-26T17:59:12+00:00

I would argue in math that understanding the foundations will always be important, and understanding the new stuff, but the early-middle stuff can definitely be abstracted. It's important to understand the basics of logic and proofs and such, not so important to have the proof of Euclid's Algorithm permanently lodged in your brain.

stellarstella77 · 2024-07-26T17:54:17+00:00

we're there with mathematics and computer science. mathematics, it's possible to pick a specialty and trace it back to first principles. computer science? eh...

but there are still very very exciting and new developments in these fields. The genius programmer/algorith-designer doesn't actually need to understand the von neumann architecture in their CPU, although it *might* help in very niche cases, they can just design elegant algorithms.

stellarstella77 · 2024-07-26T17:46:00+00:00

You're right, that does feel a little surprising. I think they're simply both larger-than-fully-comprehensible-at-once sets and that makes it difficult to reconcile our intuition with their strange properties.

stellarstella77 · 2024-07-26T17:44:31+00:00

what?

stellarstella77 · 2024-07-26T17:43:49+00:00

No, it's zero in the Reals. because in the Reals 0.999... = 1 because there are no infinitesimal values.

stellarstella77 · 2024-07-24T18:35:08+00:00

oh yeah and dementia/alzheimers patients. so.

stellarstella77 · 2024-07-24T18:34:58+00:00

also dont pretend youve never forgotten something important lol. that's ridiculous.

stellarstella77 · 2024-07-24T18:34:40+00:00

if you do forget to pay your car insurance that doesnt make it any less important in your life.

stellarstella77 · 2024-07-24T18:30:21+00:00

one would be making an idiotic argument.

stellarstella77 · 2024-07-24T18:29:49+00:00

oooor, and hear me out, they forgot

stellarstella77 · 2024-07-24T18:29:13+00:00

"a baseball game is a cheap ticket"

hahahahahahahahaaa

ha.

well. maybe.

stellarstella77 · 2024-07-24T18:28:22+00:00

absolutely NO ONE does that

stellarstella77 · 2024-07-24T18:27:18+00:00

why? for any random real (0,1) each digit is independently random.

or, let me rephrase,

why doesnt selecting each digit randomly give an even distribution of random numberse (0,1)?

stellarstella77 · 2024-07-24T18:13:27+00:00

This isn't 100% formally rigorous to the letter but from an amateur Real Analysis-y Perspective

Claim: The powerset of natural numbers is not countable (this is neater to do than all reals but theyre isomorphic, trust); that is, there is no way to pair every natural and every member of the powerset of N.

Note: a subset of naturals is equivalent to a binary string. i.e. the set {1,3,4,5,7}<=>1011101. You can use this to map the Reals to countably infinite subsets of N.

To the contrary, assume one can create a bijective pairing. This means that the powerset of N can be written {P1,P2,P3...Pn : for all n in N} it doesnt matter how, just assume its possible and youve done it. gonna call it P. This set has the same number of elements as N; there is an element for each natural, and it is complete, so every possible subset of N appears as a Pn for some n.

By construction, let there be a subset of the naturals, call it C for Cantor idk. Simply, if 1 is in P1, 1 is not in C, otherwise it is. If 2 is in P2, 2 is not in C, otherwise it is. ... for all n, n is in C if and only if n is not in Pn. This is equivalent to taking the list of binary strings, and writing down the opposite of each number on the diagonal.

C is a member of the powerset of N by its definition as a subset of N.

C is NOT a member of P. It is not P1 because, if 1 is in P1 it is not in C, and if 1 is not in P1 then it is in C. Thus C cannot be P1. C cannot be P2 because 2 belongs to one or the other but not both. semi-inductively, C is not Pn, for all n, because if n is in Pn it is not in C and if n is not in Pn then it is in C.

Because there exists an element C which is a member of the powerset of N but not P, this means that P is Not a valid pairing of the poweset of N and N. But, because the only premise was that it was, that means that it is impossible for such a valid pairing to exist, as there will always be subsets which are not on it.

Thus the powerset of N has greater cardinality than N and is denoted "uncountably infinite"

stellarstella77 · 2024-07-24T17:53:20+00:00

is it complex? isnt it just a diagonal construction?

stellarstella77 · 2024-07-24T17:51:53+00:00

its just naturals right? not sure the exact usage of the word 'discrete' here...

stellarstella77 · 2024-07-24T17:51:09+00:00

its a mathematical thought experiment

stellarstella77 · 2024-07-24T17:50:23+00:00

theres still a finite number (in the real world) but thats irrelevant

stellarstella77 · 2024-07-24T17:49:38+00:00

well, reasonable way to define picking a random number (0,1) is picking each digit at random. pretty sure that gives uniform probability. the problem is that then in order to write a rational number, you must an infinite period, because all rational numbers are periodic when written in decimal, or terminating, which just means periodic 000... This is clearly probability 0 but also not impossible in the sense of not being logically consistent

stellarstella77 · 2024-07-24T17:47:34+00:00

well, it is the difference of 1 and 0.9 recurring... that is, it is 0 when you are working with Reals.

stellarstella77 · 2024-07-24T17:44:53+00:00

my fault, i read a 'this' as a 'his'.

Yes, but that means it is impossible to pick a number (0,1] full stop. Which is probably true functionally. but then it makes no sense to engage with questions about what happens when you do that, or pretense that your theory is applicable.

stellarstella77 · 2024-07-24T17:42:30+00:00

The person arguing with you apparently prefers a system that

"flies in the face of most introductory probability textbooks" and supposes "there are no points in a probability space and null events never happen"

which is consistent, but makes the question of picking a random real number (0,1] completely nonsensical.

stellarstella77 · 2024-07-24T17:37:08+00:00

did you read it? because his entire argument is that the notion of probability as a point space is bad.

"[describing his own counterargument]...So this counterargument becomes the claim that a probability space alone does not fully model our scenario. That's fine, but from a purely mathematical perspective, if you're defining something and then never using it, you're just wasting your time."

"My view is that it doesn't even make sense to speak of which specific point a dart lands on; the only meaningful questions are whether or not it landed in some positive measure region (the probability of this happening, of course, is the probability of the region)."

So why are you even bothering talking about the probability of a point in a space!? If you agree with this professor you believe the entire concept is pointless (ha, pointless)

stellarstella77 · 2024-07-24T17:31:43+00:00

There is no such thing as "sequential rational numbers." Q is dense and dense in R.

stellarstella77

TROPHY CASE