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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
Can Hilberts grand hotel accommodate *infinite* layers of infinity? Infinite layers of nesting Although a room can be found for any finite number of nested infinities of people, the same is not always true for an infinite number of layers, even if there are a finite number of people that exist at each layer
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
linear algebra - What, exactly, does it take to make an infinite . . . If your infinite dimensional space has an inner product and is complete with respect to the induced norm then it is an infinite dimensional Hilbert space That's all it takes to make an infinite dimensional Hilbert space
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