- 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
- elementary set theory - What do finite, infinite, countable, not . . .
What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 12 years, 11 months ago Modified 12 years, 11 months ago
- Example of infinite field of characteristic $p\\neq 0$
Can you give me an example of infinite field of characteristic p ≠ 0 p ≠ 0? Thanks
- 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
- linear algebra - What can be said about the dual space of an infinite . . .
The dual space of an infinite-dimensional vector space is always strictly larger than the original space, so no to both questions This was discussed on MO but I can't find the thread
- If $S$ is an infinite $\\sigma$ algebra on $X$ then $S$ is not countable
6 Show that if a σ σ -algebra is infinite, that it contains a countably infinite collection of disjoint subsets An immediate consequence is that the σ σ -algebra is uncountable
- 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
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