(October 12, 2012 at 11:22 pm)Categories+Sheaves Wrote:(October 10, 2012 at 6:07 am)jonb Wrote: I think I may have distilled my difficulty.The sense in which you're using series is still not entirely clear to me. But are these two things equivalent as sets? If we're talking about all the real numbers between 6 and 7 or all the relevant points in such-and-such region of euclidean space, then no, the first set is strictly bigger than the second one.
Is a series of all the numbers between two points say 6 to 7 thought of as the same as say an infinity of (to use Cantor) multiples of three? Are these thought of as different categories of series?
I don't think they are the same sort of series.
Erm, what? There are as many points in R as there are in R x R x ... x R, and there are just as many points in [6,7] as there are in R. So the sets have equal cardinality.
Unless I've missed something!
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