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.
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.
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.
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.
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.