- 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
- 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
- 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
- I have learned that 1 0 is infinity, why isnt it minus infinity?
An infinite number? Kind of, because I can keep going around infinitely However, I never actually give away that sweet This is why people say that 1 0 "tends to" infinity - we can't really use infinity as a number, we can only imagine what we are getting closer to as we move in the direction of infinity
- Is there a case infinite p-group is meaningful?
An infinite dimensional vector space over a field with p p elements is probably the simplest example But there are some really wacky groups called "Tarski Monsters" that provide examples of infinite simple groups with every proper, non-trivial subgroup of order p p
- 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
- 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
- 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
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