Is this conception of countable vs. uncountable infinity adequate ...
Jan 1, 2017 · Not to mention, it is far from useful to prove more complicated cardinalities and ones of actual mathematical interest. If you want to actually understand "cardinality" and countable …
Uncountable vs Countable Infinity - Mathematics Stack Exchange
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 …
cardinals - Why is $\ {0,1\}^ {\Bbb N}$ uncountable?
May 16, 2024 · We know the interval [0, 1] [0, 1] is uncountable. You can think of the binary expansions of all numbers in [0, 1] [0, 1]. This will give you an uncountable collection of …
Proof that a non-empty perfect set is uncountable
Dec 3, 2025 · There is something I don't understand about the proof that non-empty perfect sets are uncountable. The same proof is present in Rudin's Principles of Mathematical Analysis. Do …
set theory - What makes an uncountable set "uncountable"?
Jun 4, 2023 · And since $\aleph_0$ is the cardinality of any countable set, this means that this power set must be uncountable. Some other ways to construct infinite sets are simply to add …
Uncountable Summation of Zeros - Mathematics Stack Exchange
Nov 5, 2023 · Whether the uncountable sum of zeros is zero or not simply depends on the definition of uncountable sum you're using. After all, concepts in mathematics require formal …
elementary set theory - Intersection of countable and uncountable …
Jun 24, 2018 · Countable. Uncountable. Countable or uncountable. Finite. At most countable. I understand it has to be countable, that is option 3. But the answer given was option 7 - "at …
Proving a set is uncountable - Mathematics Stack Exchange
A set $A$ is countable if $A\approx\mathbb {N}$, and uncountable if it is neither finite nor countably infinite.
An easy to understand definition of $\\omega_1$?
The problem is that one can go on like this forever without generating an uncountable ordinal, and Cantor knew that there were uncountable sets. Therefore something wholly new was needed …
elementary set theory - What do finite, infinite, countable, not ...
If there is no such bijection, then we say that A A is not countable or uncountable. If there is a bijection from a finite subset of N N to the set A A then we say that A A is finite countable.