How Much You Need To Expect You'll Pay For A Good Infinite
How Much You Need To Expect You'll Pay For A Good Infinite
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SUMMARY The words "infinite" and "transfinite" are precisely the same in evaluating the dimensions of sets, though not the same in comparing Various other relations which aren't trichotomous.
$begingroup$ Primarily, you gave the answer on your own: "infinity above infinity" just isn't described Simply because it ought to be the result of limiting procedures of various nature.
Different sorts of infinities? People phrases continue to keep puzzling me. Could someone give a transparent and unambiguous definition?
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swapping infinite sum While using the logarithm for your logarithm with the infinite solution Very hot Network Questions
Plainly $alpha$ is infinite if and provided that $alpha$ is transfinite. But note that it is determined by The truth that $leq$ is trichotomous, i.e., for almost any ordinals $alpha,beta$ both $alphaleqbeta$ or $betaleqalpha$.
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user21820user21820 60.1k99 gold badges106106 silver badges270270 bronze badges $endgroup$ 2 $begingroup$ Note that you are also assuming "there is just one amount with much larger magnitude than any finite number" in order to be able to use $infty$ as a proper noun. $endgroup$
As for the problem about whether or not a function could be expressed as a sequence or not, to reply it I think you have to say anything about calculus. What I mean is always that if a "pleasant" function Infinite Craft $f(x)$ features a series representation at some extent $a$ then the collection is given by