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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
- 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
- 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
- A circle with infinite radius is a line - Mathematics Stack Exchange
So unless your conic degenerates to a double line at infinity, you get a single line as the finite portion of a conic which by definition is a circle You can compute the center of that circle using the points above, and the result will be an infinite point, indicating the infinite radius
- Prove that the union of countably many countable sets is countable.
The prime integers form an infinite set, The prime factorization theorem the problem is (eventually) reduced to observing that U = ⨆p is a prime{pn ∣ n ≥ 1} is a subset of N Note: When there are duplicates in the original sets you'll need to get the smallest index where the element occurs to define the injective mapping into U
- If $S$ is an infinite $\\sigma$ algebra on $X$ then $S$ is not countable
5 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
- Values of $\\sum_{n=0}^\\infty x^n$ and $\\sum_{n=0}^N x^n$
That is, the "infinite sum" is the limit of the "partial sums", if this limit exists If the limit exists, equal to some number S S, we say the series "converges" to the limit, and we write
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