hardmathhardmath 37.5k2020 gold badges7979 silver badges147147 bronze badges $endgroup$ 9 2 $begingroup$ No must use that there are infinitely lots of primes: the subgroups $nmathbb Z$ for each $n in mathbb N$ are all distinct as they have distinctive indices. $endgroup$
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Some have noticed that you can create the Taylor sequence for that at $r=0$. Yet another way is to employ synthetic division or polynomial extensive division. It is difficult to typeset right here, but I am going to give you the flavor as most effective I can.
Since the phrase "transfinite" signifies "past finite" (Take note the prefix "trans" suggests "further than") that's equivalent to "larger than or equivalent to every one of the finite natural figures", we determine "transfinite" as follows.
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Asaf Karagila♦Asaf Karagila 402k4747 gold badges635635 silver badges1.1k1.1k bronze badges $endgroup$ one $begingroup$ To me "transfinite" strongly connotes principles linked to ordinals, so I locate it a inadequate choice in contexts like nonstandard Investigation the place it risks contributing to misconceptions individuals have that hyperreals have some specific connection to infinite ordinals. $endgroup$