No Stupid Questions

35923 readers

928 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

[email protected]

196

What are the most mindblowing things in mathematics? (lemmy.world)

submitted 1 year ago* (last edited 1 year ago) by [email protected] to c/[email protected]

83 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

[–] [email protected] 9 points 1 year ago (1 children)

This is a common one, but the cardinality of infinite sets. Some infinities are larger than others.

The natural numbers are countably infinite, and any set that has a one-to-one mapping to the natural numbers is also countably infinite. So that means the set of all even natural numbers is the same size as the natural numbers, because we can map 0 > 0, 1 > 2, 2 > 4, 3 > 6, etc.

But that suggests we can also map a set that seems larger than the natural numbers to the natural numbers, such as the integers: 0 → 0, 1 → 1, 2 → –1, 3 → 2, 4 → –2, etc. In fact, we can even map pairs of integers to natural numbers, and because rational numbers can be represented in terms of pairs of numbers, their cardinality is that of the natural numbers. Even though the cardinality of the rationals is identical to that of the integers, the rationals are still dense, which means that between any two rational numbers we can find another one. The integers do not have this property.

But if we try to do this with real numbers, even a limited subset such as the real numbers between 0 and 1, it is impossible to perform this mapping. If you attempted to enumerate all of the real numbers between 0 and 1 as infinitely long decimals, you could always construct a number that was not present in the original enumeration by going through each element in order and appending a digit that did not match a decimal digit in the referenced element. This is Cantor's diagonal argument, which implies that the cardinality of the real numbers is strictly greater than that of the rationals.

The best part of this is that it is possible to construct a set that has the same cardinality as the real numbers but is not dense, such as the Cantor set.