Zev ChonolesZev Chonoles 132k2121 gold badges342342 silver badges555555 bronze badges $endgroup$ 8 six $begingroup$ Precisely what is the connection among these two fields? Is one a subfield of the opposite? Is the first one particular algebraically closed? $endgroup$
Consider the long division algorithm we realized in quality school, where you are generating the terms on the best separately as you are dividing the dividend from the phrase $1-r$, multiplying the newly produced time period via the divisor, subtracting, and iterating:
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I believe it is best to elaborate when infinitesimal , and appreciable finite suggests. It'd be clear from context to some but not to Many others. $endgroup$
Then we can easily see that I can indeed reach all your values among 0 and a pair of, but you may argue that now I'm lacking many of the values while in the 2nd decimal position.
As an illustration, the set of all integers is Plainly twice as massive because the list of all even integers... and however, if you only multiply the list of all integers by two, you have the set of all even integers, Therefore showing that there's just as many even integers as integers.
$begingroup$ Within the query alone, occurs The truth that you will be investigating it at an intuitive way. The answer on your intuitive question "is 2x = x?" then is Indeed. But see that x is surely an "infinite range", and so, saying that two instances infinite is infinite isn't a giant offer.
How would you obtain the worth of `colorscheme` command to ensure it can be used as an expression again right into a variable
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$begingroup$ How can a beneficial random variable $X$ which by no means normally takes on the worth $+infty$, have expected value $mathbb E [X] = +infty$?
Examples incorporate: if you're finding out calculus of real variables, you are likely using the prolonged real line; should you be quantifying the quantity of elements in a set, you're in all probability utilizing the cardinal numbers.
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YirmidokuzYirmidokuz 14711 gold badge22 silver badges88 bronze badges $endgroup$ 3 $begingroup$ Are you acquainted with Taylor series? Series remedies of differential equations at common factors? From what foundation/qualifications do you think you're approaching this issue? $endgroup$
– Qiaochu Yuan Commented Aug 21, 2012 at 23:forty six six $begingroup$ @saadtaame, I think that what Qiaochu is trying to communicate you is always that if there is some facts in Wikipedia, let alone in many A large number of other web pages in the world wide web, Then you definitely shoud 1st test to understand there a couple of items about your Infinite Craft very own issue, lest folks Feel you are also lazy to do that by yourself . $endgroup$