EXAMPLE OF INFINITE FIELD OF CHARACTERISTIC $P\\NEQ 0$
May 11, 2023 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 math.stackexchange.com
DOES INFINITE EQUAL INFINITE? - MATHEMATICS STACK EXCHANGE
(the principal exception I know of is the extended hyperreal line, which has many infinite numbers obeying the 'usual' laws of arithmetic, and a pair of additional numbers we call $+\infty$ and $ … From math.stackexchange.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 math.stackexchange.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 math.stackexchange.com
LINEAR ALGEBRA - DEFINITION OF INFINITE DIMENSIONAL VECTOR SPACE ...
Sep 24, 2020 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 … From math.stackexchange.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 math.stackexchange.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 math.stackexchange.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 math.stackexchange.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 math.stackexchange.com
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