IF $S$ IS AN INFINITE $\\SIGMA$ ALGEBRA ON $X$ THEN $S$ IS NOT …
6 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. From bing.com
PROVE THAT THE UNION OF COUNTABLY MANY COUNTABLE SETS IS COUNTABLE.
Dec 12, 2013 I am doing some homework exercises and stumbled upon this question. I don't know where to start. Prove that the union of countably many countable sets is countable. Just … From bing.com
CALCULUS - INFINITE GEOMETRIC SERIES FORMULA DERIVATION
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. From bing.com
WHAT IS THE DIFFERENCE BETWEEN "INFINITE" AND "TRANSFINITE"?
Jun 6, 2020 The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about $\infty$ or infinite cardinals … From bing.com
LINEAR ALGEBRA - WHAT CAN BE SAID ABOUT THE DUAL SPACE OF AN …
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. From bing.com
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 … From bing.com
HOW CAN I DEFINE $E^X$ AS THE VALUE OF INFINITE SERIES?
Are you familiar with Taylor series? Series solutions of differential equations at regular points? From what foundation/background are you approaching this problem? From bing.com
ELEMENTARY SET THEORY - WHAT DO FINITE, INFINITE, COUNTABLE, NOT ...
What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 12 years, 11 months ago Modified 12 years, 11 months ago From bing.com
WHAT IS INFINITY DIVIDED BY INFINITY? - MATHEMATICS STACK EXCHANGE
Aug 11, 2012 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 … From bing.com
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