But besides historical explanations to carry out with battling with hidebound modes of considered (and I am knowledgeable about Cantor's difficulties with Kronecker and those of his strategy for considering), does there exist a concrete definition that you can go to that says: "
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10 $begingroup$ @saadtaame: due to the fact reading through Wikipedia doesn't involve inquiring Others to do Focus on your behalf. $endgroup$
without having using Taylor sequence. more explicitly devoid of utilizing calculus. how can We all know if a operate can be expressed as sequence or not ?
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Does there exist an infinite discipline with attribute $p$ for virtually any key $p$ that isn't as well big? ninety six
A further crucial case in point is $overline mathbb F _p $, the algebraic closure of your finite industry $mathbb File _p$. Should you settle for, for the moment, that every industry has an algebraic closure (which can be unquestionably not an apparent assertion), then The actual fact Infinite Craft that there are no finite algebraically shut fields ensures that the algebraic closure of a subject of characteristic $p$ will have to be an infinite subject of characteristic $p$.
$begingroup$ The evidence specified is suitable, and i am suggesting an alternate just for the sake of style/clarity (that's extra subjective than correctness).
What this means is "infinite" and "transfinite" are the identical in comparing the scale of sets. But are "infinite" and "transfinite" precisely the same in other circumstances? Let us initially take into account the regular $leq$ relation in textbooks about set idea.
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drhabdrhab 153k1111 gold badges8686 silver badges219219 bronze badges $endgroup$ 1 $begingroup$ Properly, apparent reply. $endgroup$
We make reference to the extension as a single entity via the expression $L/K$ (this is simply not a quotient such as this or this, although). An extension $L/K$ is an algebraic extension when each individual