this post was submitted on 03 Aug 2023
623 points (97.4% liked)

No Stupid Questions

35875 readers
2721 users here now

No such thing. Ask away!

!nostupidquestions is a community dedicated to being helpful and answering each others' questions on various topics.

The rules for posting and commenting, besides the rules defined here for lemmy.world, are as follows:

Rules (interactive)

Rule 1- All posts must be legitimate questions. All post titles must include a question.

All posts must be legitimate questions, and all post titles must include a question. Questions that are joke or trolling questions, memes, song lyrics as title, etc. are not allowed here. See Rule 6 for all exceptions.

Rule 2- Your question subject cannot be illegal or NSFW material.

Your question subject cannot be illegal or NSFW material. You will be warned first, banned second.

Rule 3- Do not seek mental, medical and professional help here.

Do not seek mental, medical and professional help here. Breaking this rule will not get you or your post removed, but it will put you at risk, and possibly in danger.

Rule 4- No self promotion or upvote-farming of any kind.

That's it.

Rule 5- No baiting or sealioning or promoting an agenda.

Questions which, instead of being of an innocuous nature, are specifically intended (based on reports and in the opinion of our crack moderation team) to bait users into ideological wars on charged political topics will be removed and the authors warned - or banned - depending on severity.

Rule 6- Regarding META posts and joke questions.

Provided it is about the community itself, you may post non-question posts using the [META] tag on your post title.

On fridays, you are allowed to post meme and troll questions, on the condition that it's in text format only, and conforms with our other rules. These posts MUST include the [NSQ Friday] tag in their title.

If you post a serious question on friday and are looking only for legitimate answers, then please include the [Serious] tag on your post. Irrelevant replies will then be removed by moderators.

Rule 7- You can't intentionally annoy, mock, or harass other members.

If you intentionally annoy, mock, harass, or discriminate against any individual member, you will be removed.

Likewise, if you are a member, sympathiser or a resemblant of a movement that is known to largely hate, mock, discriminate against, and/or want to take lives of a group of people, and you were provably vocal about your hate, then you will be banned on sight.

Rule 8- All comments should try to stay relevant to their parent content.

Rule 9- Reposts from other platforms are not allowed.

Let everyone have their own content.

Rule 10- Majority of bots aren't allowed to participate here.

Credits

Our breathtaking icon was bestowed upon us by @Cevilia!

The greatest banner of all time: by @TheOneWithTheHair!

founded 1 year ago
MODERATORS
ja2@lemmy.world
_MoveSwiftly@lemmy.world
Rooki@lemmy.world
Thekingoflorda@lemmy.world
automodbeta@lemmy.world
L3s@lemmy.world
623
What are the most mindblowing things in mathematics? (lemmy.world)
submitted 1 year ago* (last edited 1 year ago) by cll7793@lemmy.world to c/nostupidquestions@lemmy.world
236 comments fedilink hide all child comments
 

What concepts or facts do you know from math that is mind blowing, awesome, or simply fascinating?

Here are some I would like to share:

  • Gödel's incompleteness theorems: There are some problems in math so difficult that it can never be solved no matter how much time you put into it.
  • Halting problem: It is impossible to write a program that can figure out whether or not any input program loops forever or finishes running. (Undecidablity)

The Busy Beaver function

Now this is the mind blowing one. What is the largest non-infinite number you know? Graham's Number? TREE(3)? TREE(TREE(3))? This one will beat it easily.

  • The Busy Beaver function produces the fastest growing number that is theoretically possible. These numbers are so large we don't even know if you can compute the function to get the value even with an infinitely powerful PC.
  • In fact, just the mere act of being able to compute the value would mean solving the hardest problems in mathematics.
  • Σ(1) = 1
  • Σ(4) = 13
  • Σ(6) > 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10 (10s are stacked on each other)
  • Σ(17) > Graham's Number
  • Σ(27) If you can compute this function the Goldbach conjecture is false.
  • Σ(744) If you can compute this function the Riemann hypothesis is false.

Sources:

you are viewing a single comment's thread
view the rest of the comments
[–] Barack_Embalmer@lemmy.world 14 points 1 year ago* (last edited 1 year ago) (2 children)

There are many structures of proof. A simple one might be to prove a statement is true for all cases, by simply examining each case and demonstrating it, but as you point out this won't be useful for proving statements about infinite cases.

Instead you could assume, for the sake of argument, that the statement is false, and show how this leads to a logical inconsistency, which is called proof by contradiction. For example, Georg Cantor used a proof by contradiction to demonstrate that the set of Natural Numbers (1,2,3,4...) are smaller than the set of Real Numbers (which includes the Naturals and all decimal numbers like pi and 69.6969696969...), and so there exist different "sizes" of infinity!

For a method explicitly concerned with proofs about infinite numbers of things, you can try Proof by Mathematical Induction. It's a bit tricky to describe...

  • First demonstrate that a statement is true in some 1st base case.
  • Then demonstrate that if it holds true for the abstract Nth case, then it necessarily holds true for the (N+1)th case (by doing some clever rearranging of algebra terms or something)
  • Therefore since it holds true for the 1th case, it must hold true for the (1+1)th case = the 2th case. And since it holds true for the 2th case it must hold true for the (2+1)=3th case. And so on ad infinitum.

Wikipedia says:

Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes.

Bear in mind, in formal terms a "proof" is simply a list of true statements, that begin with axioms (which are true by default) and rules of inference that show how each line is derived from the line above.

[–] madcaesar@lemmy.world 2 points 1 year ago

Very cool and fascinating world of mathematics!

[–] HappySquid@feddit.ch 1 points 1 year ago

Just to add to this. Another way could be to find a specific construction. If you could for example find an algorithm that given any even integer returns two primes that add up to it and you showed this algorithm always works. Then that would be a proof of the Goldbach conjecture.