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Thread: ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")
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face BY : 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?

No.
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,

Ok

>     then 0.999... EQUALS 1 when the number of 9s EQUALS infinity.

No.
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
the carpet.

> > 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.


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Subject (change) ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")

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