this post was submitted on 03 Aug 2023
516 points (97.1% liked)

No Stupid Questions

36168 readers
1738 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 2 years ago
MODERATORS
ja2@lemmy.world
_MoveSwiftly@lemmy.world
Rooki@lemmy.world
Thekingoflorda@lemmy.world
automodbeta@lemmy.world
L3s@lemmy.world
516
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
172 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
[–] Badland9085@lemm.ee 6 points 1 year ago (1 children)

You are correct. This notion of “size” of sets is called “cardinality”. For two sets to have the same “size” is to have the same cardinality.

The set of natural numbers (whole, counting numbers, starting from either 0 or 1, depending on which field you’re in) and the integers have the same cardinality. They also have the same cardinality as the rational numbers, numbers that can be written as a fraction of integers. However, none of these have the same cardinality as the reals, and the way to prove that is through Cantor’s well-known Diagonal Argument.

Another interesting thing that makes integers and rationals different, despite them having the same cardinality, is that the rationals are “dense” in the reals. What “rationals are dense in the reals” means is that if you take any two real numbers, you can always find a rational number between them. This is, however, not true for integers. Pretty fascinating, since this shows that the intuitive notion of “relative size” actually captures the idea of, in this case, distance, aka a metric. Cardinality is thus defined to remove that notion.

[–] TheGiantKorean@lemmy.world 3 points 1 year ago* (last edited 1 year ago)

Fantastic explanation. Thank you!

Edit: I guess I should have said rational numbers vs real. I just looked up the difference.