heropupheropup 143k1515 gold badges113113 silver badges200200 bronze badges $endgroup$ 2 $begingroup$ Do you've got any information about the main just one who proved this? $endgroup$

Think about the lengthy division algorithm we figured out in quality college, where you are generating the conditions on the best one after the other as you might be dividing the dividend via the term $one-r$, multiplying the newly produced term with the divisor, subtracting, and iterating:

This is absolutely what we initially intended when we stated $T$ is definitely an "indeterminate" - it stands in no relation to $mathbb F _p$, We've got only additional it in as a proper image, so the one way we can get

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The main reason staying, specifically in the non-typical Assessment case, that "infinite variety" is sort of uncomfortable and could make people contemplate $infty$ or infinite cardinals by some means, which can be providing the incorrect impact.

In other situations of divergent integrals or sequence, the regularized value and/or development fee (germ at infinity) or conduct at a singularity can differ as well or the distinctions can compensate for each other as in the example over.

Be aware that someone may define "transfinite" similar to "Dedekind infinite" that's an abuse of words for my part.

The alephs are a very unrelated Idea: cardinal numbers (and ordinal figures, for that matter) don't have anything to try and do with that subject. $endgroup$

The purpose from the OP's proof exactly where an in depth argument seems is nested Within the circumstance Examination (finitely several vs. infinitely lots of cyclic subgroups). Pulling that argument out as a Lemma serves both equally to motivate The end result also to simplify the leading argument that follows:

This suggests "infinite" and "transfinite" are the exact same in comparing the size of sets. But are "infinite" and "transfinite" a similar in other circumstances? Infinite Craft Let's to start with look at the normal $leq$ relation in textbooks about established principle.

What's the best way to explain the most crucial traces with the WoD to a complete newbie without smacking them While using the e book?

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in concrete manner and distinguish a number of circumstances depending upon the nature of numerator and denominator: infinitesimal, infinite, or appreciable finite, ahead of speaking about the technical notion of Restrict which has a tendency to be confusing to novices.

– Qiaochu Yuan Commented Aug 21, 2012 at 23:46 6 $begingroup$ @saadtaame, I think that what Qiaochu is trying to communicate you is that if there's some info in Wikipedia, let alone in numerous Many other sites in the web, Then you definitely shoud initial attempt to discover there a couple of factors regarding your possess problem, lest persons Consider you happen to be way too lazy to do this by oneself . $endgroup$