- 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
- Finding a basis of an infinite-dimensional vector space?
The other day, my teacher was talking infinite-dimensional vector spaces and complications that arise when trying to find a basis for those He mentioned that it's been proven that some (or all, do
- Questions about the Infinite Monkey Theorem - Mathematics Stack Exchange
(Context: the Infinite Monkey Theorem stipulates that given infinite time, a monkey can type out the complete works of Shakespeare, or any other text of finite length, just by randomly pressing key
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 2 months ago Modified 4 years, 5 months ago
- 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
- elementary set theory - What do finite, infinite, countable, not . . .
A set A A is infinite, if it is not finite The term countable is somewhat ambiguous (1) I would say that countable and countably infinite are the same That is, a set A A is countable (countably infinite) if there exists a bijection between A A and N N (2) Other people would define countable to be finite or in bijection with N N
- Subspaces of an infinite dimensional vector space
If V V is an infinite dimensional vector spaces, then it has an infinite basis Any proper subset of that basis spans a proper subspace whose dimension is the cardinality of the subset So, since an infinite set has both finite and infinite subsets, every infinite dimensional vector space has both finite and infinite proper subspaces
- 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
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