www.piclist.com/techref/index.htm?key=brain+burp+rounding

>

> 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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