ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")
David VanHorn email (remove spam text)
> What if I said that the DEFINITION of "infinite" is "the number
> of 9s you'd have to append to 0.9 in order to make that number
> equal to 1"? Would that make sense?
If, at any point we can just say "aw to hell with it, it's almost 1, so
it's 1", I have a problem with that.
However, as a tool in calculus, to allow calculations that wouldn't
otherwise be possible, and with the proviso that we are approximating, and
not exactly calculating an answer, I have no problem with it.
The root problem here appears to be that there some numbers which the
decimal system is ill equipped to represent, in a manner similar to roman
numerals having problems with large numbers, only in a deeper manner.
1/3 is easy to deal with, but can't be represented with complete accuracy
in decimal form.
> Perhaps you could look at it in this casual, common-sense way:
> If 0.999... APPROACHES 1 as the number of 9s APPROACHES infinity,
> then 0.999... EQUALS 1 when the number of 9s EQUALS infinity.
I see no requirement that it do so.
> Feynman hasn't been having trouble with ANY calculations since
> he died, and if Hawking could speak, I'm pretty sure he'd tell
> you that 0.999... is equal to 1.
For any practical matter, yes.
However, in an absolute sense, this is just sweeping some ugliness under
> > It wasn't that long ago that "zero" didn't exist in mathmatics.
> "Zero" has ALWAYS existed in mathematics: "If Julius has X
> apples, and he gives III to Brutus and VII to Biggus Dickus, how
> many apples remain?"
If you can't represent it, then you can't do calculations with it.
Dave's Engineering Page: http://www.dvanhorn.org
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