Wacek Kusnierczyk wrote: > Peter Dalgaard wrote: > >> Stefan Evert wrote: >> >> >>> ... am I the only one who thinks that the integer 7 is something >>> entirely different from the real number 7.0? (The latter most likely >>> being an equivalence class of sequences of rational numbers, but that >>> depends on your axiomatisation of real numbers.) Integers can be >>> embedded in the set of real numbers, but that doesn't make them the >>> same mathematically. >>> >>> >>> >> Several people have tried to make that point (or something very >> similar), but it doesn't seem to take. >> >> It might get clearer if taken one step up: is.double(-1+0i) is not true >> either, even though the real line is cleanly embedded in complex space, >> -1+0i is not the same as -1. For instance, you can take the square root >> of the former but not the latter. >> >> > > you see, there seems to be a confusion of *numbers* and their > *representations*. > but of course the integer 7 is *the same* number as the real number 1.0, > oops, a typo; the integer 7 is the same number as the real number *7.0*. every integer is real, and the set of real numbers does not contain both the integer 7 and the real 7.0 as two distinct numbers.
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