this post was submitted on 26 Dec 2024
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Asklemmy
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It's almost sure to be the case, but nobody has managed to prove it yet.
Simply being infinite and non-repeating doesn't guarantee that all finite sequences will appear. For example, you could have an infinite non-repeating number that doesn't have any 9s in it. But, as far as numbers go, exceptions like that are very rare, and in almost all (infinite, non-repeating) numbers you'll have all finite sequences appearing.
Exceptions are infinite. Is that rare?
Yes. The exceptions are a smaller cardinality of infinity than the set of all real numbers.
Rare in this context is a question of density. There are infinitely many integers within the real numbers, for example, but there are far more non-integers than integers. So integers are more rare within the real.
There is not density in infinity
I think you mean "I don't understand density in infinity".
They should look up the classic example of rationals in the real numbers. Their statement could hardly be more wrong.
we were talking about probability
I most assuredly am talking about your false statement regarding density.
I am talking about probability with the grownups hun, later
Weird to flex when you have nothing to show off. Let me show you how you do it, buddy: I am a mathematician. Infinity, density and cardinality of sets are not mysterious to me because I read a lot of books. If you read a few then you might discover your very cool comment above was actually not so cool and true.
It is true in the probability problem we talked about, and it's not a statement, it's not a thesis, it's an attempt at conversation between emotionally stable adults but it is really okay to be autistic just don't make fights over it because it's no big deal for anyone else that all statements are perfect but that they get meaning across
Damn, you really do suck more as a person than you do at math.
Yes, compared to the infinitely more non exceptions. For each infinite number that doesn't contain the digit 9 you have an infinite amount of numbers that can be mapped to that by removing all the 9s. For example 3.99345 and 3.34999995 both map to 3.345. In the other direction it doesn't work that way.
Very rare in the sense that they have a probability of 0.
There are lot that fit that pattern. However, most/all naturally used irrational numbers seem to be normal. Maths has, however had enough things that seemed 'obvious' which turned out to be false later. Just because it's obvious doesn't mean it's mathematically true.