Post an interesting (to you) math theorem or fact, at any level of obscurity. I'll post a relatively mainstream one

>the continuum hypothesis is independent of ZFC axioms

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# Post an interesting (to you) math theorem or fact, at any level of obscurity. I'll post a relatively mainstream one

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>the continuum hypothesis is independent of ZFC axioms

Events with a 0% probability of occurring can occur. Events with a 100% probability of occurring can not occur.

What are you even talking about.

Events with 100% probability absolutely can occur, and in fact definitionally must be able to occur. As an example, let the event A be "the coin lands on heads or tails," in the classical fair coin flip experiment. This is the sure event. It has to occur and has 100% probability.

No, can "not occur", not "can not" occur. I'd have said "can't" occur or "cannot" occur if I meant "can not" occur instead of can "not occur". Isn't English fun?

Can you give an example with P{A} = 1 that isn't actually sure to occur? That seems like a problem with the definition of the probability measure, not something that is fundamental to probability theory.

It has to do with natural density. The limiting behavior of probabilities can tend towards 0, while still converging to an event which is possible.

I understand the point probability being zero for any continuous density (as all points masses are in sets of Lebesgue measure zero). The one I don't get is the event with probability 1 that doesn't occur. This converse is one I don't understand.

X is uniformly distributed in [0,1], A is "X =/= 1/2"

Thank you. For some reason the concept looking a the complement of a point event hadn't crossed my mind. I'm also kind of moronic and it's the middle of the night, so that doesn't help.

In fairness, probability isn't exactly intuitive.

Let's say you choose a random number from 0 to 1. What is the probability you choose a number other than .5? Can you choose .5?

here’s a fun one: almost all numbers contain a 3 in its digits. so if you pick a random number, theres a 100% chance it will contain a 3.

Even more fun: if a computer picks a random number, there's a 0% chance it will contain a 3.

>t. missed the point entirely

KEK! Oh, this website...

>Events with a 0% probability of occurring can occur.

Then it's not 0%, Even if it's a simple on/off, yes/no, either/or question an event with 49,999% probability does not occur

Let 0% - 50% = not occur

Let 50% - 100% = occur

Only a perfect 50% the event can either occur or not if the question is only 2 sided like the question is (occurs or not)

5/3 is a fundamental constant for turbulence, which is strange.

>Le most beautiful equation in mathematics

0.999... != 1

I'll do you one better

These may be more math history facts (as I am not a learned STEMcel), but it is interesting anyway:

In his late life, Euler went blind, but with the help of scribes he managed to author an average of one paper per week nonetheless. He was a fervent and fiery Christian--known for getting into heated debates with atheists of his day, and yet he had the entirety of the Iliad memorized to page and line. Fascinating man.

>Accurate reckoning -- the entrance into the knowledge of all existing things and all obscure secrets. ~ Ahmes the Scribe, 17th century BC

The Babylonians used a sexigesimal system--their base number was 60, rather than 10.

The French actually used metric time for a while

I always liked the idea of non-transitive dice. There exist ways of labeling the faces of sets of dice such that the first die beats the 2nd on average, the 2nd beats the 3rd on average, and the 3rd beats the 1st on average.

oh, neat

There is a subset A (green) of [0,1] x [0,1] such that all horizontal slices {a} x [0,1] (yellow) intersect A in only countably many points, but all vertical slices [0,1] x {b} (red) intersect A in ALL-but-countably-many points. Try to draw a better picture than this to really see how weird this is.

Of course you need the (obviously true) continuum hypothesis to prove it

1=|-i|

1/i = -i, so the additive and multiplicative inverses of i are the same.

oh