this post was submitted on 03 Aug 2023

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No Stupid Questions

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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]

233 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:

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[–] [email protected] 70 points 1 year ago (11 children)

I came here to find some cool, mind-blowing facts about math and have instead confirmed that I'm not smart enough to have my mind blown. I am familiar with some of the words used by others in this thread, but not enough of them to understand, lol.

[–] [email protected] 12 points 1 year ago (7 children)

Same here! Great post but I'm out! lol

[–] [email protected] 8 points 1 year ago (4 children)

Nonsense! I can blow both your minds without a single proof or mathematical symbol, observe!

There are different sizes of infinity.

Think of integers, or whole numbers; 1, 2, 3, 4, 5 and so on. How many are there? Infinite, you can always add one to your previous number.

Now take odd numbers; 1, 3, 5, 7, and so on. How many are there? Again, infinite because you just add 2 to the previous odd number and get a new odd number.

Both of these are infinite, but the set of numbers containing odd numbers is by definition smaller than the set of numbers containing all integers, because it doesn't have the even numbers.

But they are both still infinite.

[–] [email protected] 2 points 1 year ago* (last edited 1 year ago)

Both of these are infinite, but the set of numbers containing odd numbers is by definition smaller than the set of numbers containing all integers, because it doesn't have the even numbers.

This is provably false - the two sets are the same size. If you take the set of all integers, and then double each number and subtract one, you get the set of odd numbers. Since you haven't removed or added any elements to the initial set, the two sets have the same size.

The size of this set was named Aleph-zero by Cantor.

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