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| In a message dated 10/30/2002 9:03:32 AM Central Standard Time, cowan@hidden.email writes: << I don't agree. Every natural number is an integer; every integer is a >> Gee, I'm trying to think of a branch of mathematics in which this claim is true. Certainly not in any of my areas: set theory, computation theory, computer science (honorary), Grundlagensforchungen generally. Nor, I think, in the numerical disiplines: arithmetic is incomplete and undecidable, analysis is at least complete, so, if integers were real numbers, we could complete arithmetic by going through analysis (only slightly specious argument). We do -- outside of computer work and very fussy projects -- tend to use the same notation for the lot (as the rationals get totally absorbed into the reals, while still being very different things -- sets of ordered pairs, vs. ordered pairs of sets, for example). And, of course there is an identity relation for numbers finer than equality, namely ontic identity, which requirtes that they be the same thing, not merely have the same value (under condition...). xorxes: << la and cusku di'e >forgive my ignorance, but how come 21.9999999999999 is equal to >22.0? One way of seeing it is this: x = 21.9999... 10x = 219.9999... 10x - x = 198.0000... 9x = 198 x = 198/9 x = 22 >> Nice, if contradictory looking. Certainly more intelligible (and so convincing) than the usual one through the calculus. |