- 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 I subtract infinity from infinity? - Mathematics Stack Exchange
Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like limn→∞(1 + x n)n, lim n → ∞ (1 + x n) n, or is it just a parlor trick for a much easier kind of limit?
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
The two are effectively equivalent but the second method views the infinite series as a sequence of partial sums, which is more amenable to proofs and is more rigorous
- elementary set theory - What do finite, infinite, countable, not . . .
A set 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 is countable (countably infinite) if there exists a bijection between A and N (2) Other people would define countable to be finite or in bijection with N
- What exactly is infinity? - Mathematics Stack Exchange
The infinite manifold of two or three dimensions, the mathematical beings which depend on a number of variables greater even than three, any number in fact, still have no greater power than the linear continuum
- 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?
Infinite simply means "not finite", both in the colloquial sense and in the technical sense (where we first define the term "finite") There is no technical definition that I am aware of for "transfinite" Nevertheless, I can attest to my personal use Transfinite is good when there is a notion of order, so "transfinite ordinal", or when you want to talk about non-standard real numbers which
- linear algebra - Definition of Infinite Dimensional Vector Space . . .
In the text i am referring for Linear Algebra , following definition for Infinite dimensional vector space is given The Vector Space V(F) is said to be infinite dimensional vector space or infin
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