Nov 5, 2015 · My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural numbers is

Feb 28, 2022 · I once called a dense set an uncountable set. I was told this was wrong, as the set was dense, and not uncountable. I didn't have the mathematical knowledge to find this confusing, and …

Aug 10, 2024 · The image of discrete random variable X X is the union of its countable support and a null set, which can be countable or uncountable. Note that K K is not unique and can be any …

A set $A$ is countable if $A\approx\mathbb {N}$, and uncountable if it is neither finite nor countably infinite.

Nov 25, 2020 · A simple way to see that the cantor set is uncountable is to observe that all numbers between 0 0 and 1 1 with ternary expansion consisting of only 0 0 and 2 2 are part of cantor set. …

Dec 5, 2015 · I am having trouble with the following terms: countably infinite, uncountable, and finite. In addition, for the following problems I need to select which category they fall into. $1)$ Consider a s...

Jul 5, 2016 · What's the definition of countable and uncountable. This simply cries out to me that we must find a 1-1 correspondence between (0,1) and R.

Mar 9, 2015 · How to find an uncountable subset of P(N) P (N) such that every two elements of it can be compared. In fact, give an uncountable subset of P(N) P (N) such that has totality property. We mean …

The number which is the diagonal is transformed s.t. it doesn't share the first digit of the first number nor the second digit with the second and so on. Thus the number is unique to the list. This is why …

Dec 15, 2015 · The canonical proof that the Cantor set is uncountable does not use Cantor's diagonal argument directly. It uses the fact that there exists a bijection with an uncountable set (usually the …