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MATHEMATICAL OPERATIONS WITH INFINITY - MATHEMATICS STACK EXCHANGE
Jan 1, 2021 Let us follow the convention that an expression with $\infty$ is "defined" (in the extended reals) if: when you replace each $\infty$ with any function/sequence whose limit is … From bing.com
EXAMPLE OF INFINITE FIELD OF CHARACTERISTIC $P\\NEQ 0$
On the other hand, if we had $\overline{\mathbb{F}_p}\subseteq\mathbb{F}_p(T)$, then we would have that there were some $\frac{f}{g}\in \mathbb{F}_p(T)$ such that … From bing.com
I HAVE LEARNED THAT 1/0 IS INFINITY, WHY ISN'T IT MINUS INFINITY?
Infinite numbers do exist in the hyperreal number system which properly extends the real number system, but then their reciprocals are infinitesimals rather than zero. Thus the idea of … From bing.com
ELEMENTARY SET THEORY - WHAT DO FINITE, INFINITE, COUNTABLE, NOT ...
Clearly every finite set is countable, but also some infinite sets are countable. Note that some places define countable as infinite and the above definition. In such cases we say that finite … From bing.com
WHAT EXACTLY IS INFINITY? - MATHEMATICS STACK EXCHANGE
Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called … From bing.com
UNCOUNTABLE VS COUNTABLE INFINITY - MATHEMATICS STACK EXCHANGE
As far as I understand, the list of all natural numbers is countably infinite and the list of reals between 0 and 1 is uncountably infinite. Cantor's diagonal proof shows how even a … From bing.com
PROOF OF INFINITE MONKEY THEOREM. - MATHEMATICS STACK EXCHANGE
Apr 24, 2015 The infinite monkey theorem states that if you have an infinite number of monkeys each hitting keys at random on typewriter keyboards then, with probability 1, one of them will … From bing.com
LIMITS - CAN I SUBTRACT INFINITY FROM INFINITY? - MATHEMATICS STACK ...
Apr 28, 2016 $\begingroup$ Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like … From bing.com
CALCULUS - WHAT IS INFINITY DIVIDED BY INFINITY? - MATHEMATICS STACK ...
Aug 11, 2012 One advantage of approach (2) is that it allows one to discuss indeterminate forms in concrete fashion and distinguish several cases depending on the nature of numerator and … From bing.com
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