I'm trying to show that the interval $(0,1)$ is uncountable and I want to verify that my proof is correct My solution: Suppose by way of contradiction that $(0, 1)$ is countable. Then we can …

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 …

Hence, the number of accumulation points is uncountable. My question is, is this logic valid? I would have to prove that an uncountable set minus a countable set is uncountable, which …

Sep 13, 2018 · In set theory, when we talk about the cardinality of a set we have notions of finite, countable and uncountably infinite sets. Main Question Let's talk about the dimension of a …

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 …

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 …

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

To prove that an infinite σ -field F is uncountable, we first establish the following lemma. Lemma: If F is an infinite σ -field, then there exists an infinite sequence of disjoint nonempty sets {Bi} ⊆ F.

May 30, 2022 · The notes then mention that this means we only need countable additivity. I understand the theorem and that this means that uncountable additivity of measures would …

A space for which any two points can be separated by a continuous real-valued function is said to be functionally Hausdorff and if it's connected and has more than two points, it's uncountable.