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- If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable
6 Show that if a $\sigma$-algebra is infinite, that it contains a countably infinite collection of disjoint subsets An immediate consequence is that the $\sigma$-algebra is uncountable
- Example of infinite field of characteristic $p\neq 0$
Can you give me an example of infinite field of characteristic $p\\neq0$? Thanks
- Infinite product of measurable spaces - Mathematics Stack Exchange
Suppose there is a family (can be infinite) of measurable spaces What are the usual ways to define a sigma algebra on their Cartesian product? There is one way in the context of defining product
- How to prove the infinite number of sides in a circle?
0 There is a way of proving that there is "infinite number of sides in a circle", in the following sense Infinity was a number to both Kepler and Leibniz who spoke of a circle as an infinite-sided polygon This point of view is useful in analyzing the properties of the circle, as well as more general curves, in infinitesimal calculus
- linear algebra - Is there a quick proof as to why the vector space of . . .
Your further question in the comments, whether a vector space over $\mathbb {Q}$ is finite dimensional if and only if the set of vectors is countable, has a negative answer If the vector space is finite dimensional, then it is a countable set; but there are infinite-dimensional vector spaces over $\mathbb {Q}$ that are countable as sets
- elementary set theory - What do finite, infinite, countable, not . . .
What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago
- Does infinite equal infinite? - Mathematics Stack Exchange
All three integrals are divergent and infinite and have the regularized value zero, but two of them are equal but not equal to the third one In other cases of divergent integrals or series, the regularized value and or growth rate (germ at infinity) or behavior at a singularity can differ as well or the differences can compensate for each
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 6 months ago Modified 4 years, 9 months ago
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