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Anonymous at Fri, 8 Mar 2024 04:48:35 UTC No. 16062322
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
Anonymous at Fri, 8 Mar 2024 04:56:20 UTC No. 16062327
Events with a 0% probability of occurring can occur. Events with a 100% probability of occurring can not occur.
Anonymous at Fri, 8 Mar 2024 04:58:19 UTC No. 16062328
>>16062327
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.
Anonymous at Fri, 8 Mar 2024 04:59:46 UTC No. 16062330
>>16062322
5/3 is a fundamental constant for turbulence, which is strange.
Anonymous at Fri, 8 Mar 2024 05:01:52 UTC No. 16062333
>>16062328
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?
Anonymous at Fri, 8 Mar 2024 05:44:54 UTC No. 16062381
>>16062333
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.
Anonymous at Fri, 8 Mar 2024 05:59:00 UTC No. 16062392
>>16062381
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.
Anonymous at Fri, 8 Mar 2024 06:13:41 UTC No. 16062397
>>16062392
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.
Anonymous at Fri, 8 Mar 2024 06:15:38 UTC No. 16062399
>>16062397
X is uniformly distributed in [0,1], A is "X =/= 1/2"
Anonymous at Fri, 8 Mar 2024 06:17:13 UTC No. 16062402
>>16062397
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?
Anonymous at Fri, 8 Mar 2024 06:20:13 UTC No. 16062405
>>16062399
>>16062402
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 retarded and it's the middle of the night, so that doesn't help.
Anonymous at Fri, 8 Mar 2024 06:21:09 UTC No. 16062406
>>16062405
In fairness, probability isn't exactly intuitive.
Anonymous at Fri, 8 Mar 2024 06:47:15 UTC No. 16062421
>>16062322
>>16062381
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.
Anonymous at Fri, 8 Mar 2024 07:10:30 UTC No. 16062452
>>16062421
Even more fun: if a computer picks a random number, there's a 0% chance it will contain a 3.
Anonymous at Fri, 8 Mar 2024 10:28:49 UTC No. 16062608
>>16062322
0.999... != 1
Anonymous at Fri, 8 Mar 2024 10:39:54 UTC No. 16062617
>>16062608
I'll do you one better
Anonymous at Fri, 8 Mar 2024 10:47:13 UTC No. 16062621
>>16062328
>t. missed the point entirely
KEK! Oh, this website...
Anonymous at Fri, 8 Mar 2024 10:54:37 UTC No. 16062627
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.
Anonymous at Fri, 8 Mar 2024 11:42:14 UTC No. 16062654
>>16062322
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.
Anonymous at Fri, 8 Mar 2024 13:16:28 UTC No. 16062726
>>16062327
>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)
Anonymous at Fri, 8 Mar 2024 14:59:48 UTC No. 16062860
>>16062608
indeed, 0.999...=1-(1776*ε)
Anonymous at Fri, 8 Mar 2024 15:02:24 UTC No. 16062865
>>16062654
oh, neat
Anonymous at Fri, 8 Mar 2024 17:40:13 UTC No. 16063155
>>16062627
The French actually used metric time for a while
Anonymous at Fri, 8 Mar 2024 19:43:47 UTC No. 16063359
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
Anonymous at Sat, 9 Mar 2024 06:51:52 UTC No. 16064529
1=|-i|
Anonymous at Sat, 9 Mar 2024 07:07:46 UTC No. 16064549
1/i = -i, so the additive and multiplicative inverses of i are the same.
Anonymous at Sat, 9 Mar 2024 19:52:05 UTC No. 16065388