New Step by Step Map For Infinite
New Step by Step Map For Infinite
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Zev ChonolesZev Chonoles 132k2121 gold badges342342 silver badges555555 bronze badges $endgroup$ eight 6 $begingroup$ Precisely what is the relationship among both of these fields? Is 1 a subfield of the opposite? Is the first one particular algebraically shut? $endgroup$
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If an infinite team $G$ is created by two factors $a,b$ this sort of that $a^n=b^n=e$, need to $x^n=e$ have infinitely several options? 0
I believe it is best to elaborate when infinitesimal , and appreciable finite suggests. It might be very clear from context to some although not to Many others. $endgroup$
For the reason that term "infinite" indicates "not finite", we get started through the definition of "finite". Considering that we can confirm
Distinctive kinds of infinities? Those terms retain complicated me. Could anyone give a clear and unambiguous definition?
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not all wrongnot all Mistaken sixteen.4k22 gold badges3737 silver badges5757 bronze badges $endgroup$ Insert a comment
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1 $begingroup$ @sos440: In NSA, infinite quantities haven't got specifiable measurements, and you can't uniquely identify a sum like $one+one+1+ldots$ with a particular hyperreal. Hyperreals may be defined as equivalence lessons of sequences underneath an ultrafilter. Due to the fact ultrafilters can't be explicitly made, You cannot, generally, take infinite sums $sum a_i$ and $sum b_i$ and say whether or not they seek advice from the exact same hyperreal.
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user21820user21820 60.1k99 gold badges106106 silver badges270270 bronze badges $endgroup$ 2 $begingroup$ Be aware you are also assuming "there is only one quantity with greater magnitude than any finite variety" as a way to have the ability to use $infty$ as a suitable noun. $endgroup$
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