heropupheropup 143k1515 gold badges113113 silver badges200200 bronze badges $endgroup$ 2 $begingroup$ Do you have any details about the 1st one who proved this? $endgroup$
$begingroup$ As drhab said in his remedy, your intuition lets you know that $infty situations 2$ really should be $infty$. But that intuition is dependent upon what you understood
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one $begingroup$ I feel Riemann Rearrangement theorem relates to conditionally convergent collection, and Because the conditions Here's all strictly optimistic, it is not applicable below(I think). $endgroup$
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It can be akin to asking, if John runs twice as fast as Jack and the two operate off faraway from me, am i able to divide John's closing place by Jack's final situation, which can be each further more from me than I'm able to ever go, and have $2=one$? (Obviously neither John nor Jack them selves can get to their "remaining situation", but the process by which they 'method' it describes your situation fairly well.)
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Considering that the word "transfinite" usually means "past finite" (Take note that the prefix "trans" usually means "beyond") which is similar to "bigger than or equivalent to every one of the finite purely natural figures", we outline "transfinite" as follows.
What this means is "infinite" and "transfinite" are the same in evaluating the dimensions of sets. But are "infinite" and "transfinite" exactly the same in other scenarios? Let us to start with look at the normal $leq$ relation in textbooks about set principle.
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2 $begingroup$ Two points that I think a freshman calc scholar needs to soak up: (one) Things we would publish as $infty/infty$ Infinite Craft are called indeterminate kinds, and calculus offers particular tactics for researching them. (2) Is infinity is actually a range? See this question: math.
in concrete vogue and distinguish several circumstances depending on the character of numerator and denominator: infinitesimal, infinite, or appreciable finite, ahead of speaking about the technological Idea of Restrict which has a tendency to be confusing to inexperienced persons.
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