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What is infinity divided by infinity? - Mathematics Stack Exchange I know that $\\infty \\infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
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 numbers is
What is the difference between infinite and transfinite? The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about ∞ ∞ or infinite cardinals somehow, which may be giving the wrong impression But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes place
De Morgans law on infinite unions and intersections Then prove that it holds for an index set of size n + 1 n + 1 and wrap it up by n → ∞ n → ∞ but I'm not convinced that's right For example, an argument like that doesn't work for countable intersection being closed on a collection of open sets So what's a good proof that can extend de Morgan's law to an infinite collection of sets
Infinite class of closed sets whose union is not closed Here is a good example which clearly shows that the infinite union of closed sets may not be closed consider the usual topology on R R, and let C C be the collection of all closed sets of the form (−∞, n n+1] (∞, n n + 1] where n ≥ 1 n ≥ 1