hardmathhardmath 37.5k2020 gold badges7979 silver badges147147 bronze badges $endgroup$ nine 2 $begingroup$ No must use that there are infinitely many primes: the subgroups $nmathbb Z$ for every $n in mathbb N$ are all distinctive given that they have unique indices. $endgroup$
Bhaskar VashishthBhaskar Vashishth 11.6k55 gold badges4444 silver badges9393 bronze badges $endgroup$ 1 4 $begingroup$ Not all that convincing, given that there are plenty of techniques such as infinite figures, so perhaps the response should be “it relies upon which infinity you are taking”. Other solutions elaborate this. $endgroup$
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$begingroup$ No, there's no these types of definition. The term "transfinite" is just not made use of whatsoever like a complex time period in modern mathematics. It really is used in a few fixed phrases: "transfinite induction" and "transfinite recursion", which make reference to induction or recursion which is indexed by a standard properly-requested established (or maybe more frequently, a set using a properly-Launched relation) rather then just normal induction within the normal quantities.
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YirmidokuzYirmidokuz 14711 gold badge22 silver badges88 bronze badges $endgroup$ 3 $begingroup$ Are you currently knowledgeable about Taylor series? Series options of differential equations at normal points? From what foundation/background are you approaching this issue? $endgroup$
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