piclist 2001\06\04\144524a >
Thread: ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")
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On Sun, Jun 03, 2001 at 11:22:48PM -0400, M. Adam Davis wrote:
>
> Of course, conceptually, 0.999... does not equal one.

Nope. It equals 1. No intents or purposes necessary.

>  It equals
> 0.999....  But using calculus and other methods you see that 0.999...
> approaches 1, and, for all intents and purposes, is equal to 1.  It
> really depends on what level of precision one is asking for.
>  If one
> want infinite precision then one cannot say that 0.999... = 1 unless one
> can prove that 0.999... approaches one faster than the needed precision
> approaches infinity.

Precision implies finiteness. It implies that there will be a cutoff of the
9's at some point in the string.

The 9's end at the same place that the largest possible integer resides. Care
to define that number?

>
> But this is all academic, and is akin to proving that the chicken came
> before the eggroll.  If anyone wants to prove me wrong, then sit down
> and write a 0, a decimal point, an infinite series of nines, and equal
> sign, and a one (no shorthand, please!) before hitting reply.

There's no need for that. The term 0.9 (repeating) is a sufficient
representation for that infinite series. Folks here are failing to grasp that
mathematics for infinity doesn't follow normal finite mathematicl rules.
Equations as simple as 'infinity*2 = infinity' are completely nonsensical
for nonfinite values but true for infinity. Any argument for precision or
truncation of infinity is akin to stating that 'The largest integer is x.'
There's simply to truth to that statement.

In infinity arithmatic 0.9 (repeating) = 1. Not approximates. No approches.
No precision. No error. The proof has been given in this thread multiple times.

I really liked the argument I saw yesterday. I'll repeat it and ask if anyone
can propose a solution: "If 0.9 (repeating) < 1, then there are an infinite
number of real numbers that exists between 0.9 (repeating) and 1. Give one
such number."

And try as you might, you'll find that there is no such number. You'll find
in your search that no matter what number you pick, it will not be between
0.9 (repeating) and 1. Therefore the two values must be the same because not
only can you not define an infinite number of real numbers between the two,
you can't even pick one.

There's no pretense here. Infinity mathematics is exact. Not approximations.
It doesn't exist in the real world, only in the concepts of our minds.

So for the refuters you now need to bring two items to the table. The largest
possible integer, and a number between 0.9 (repeating) and 1.

Good luck.

BAJ

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In reply to: <3B1AFF08.8080308@ubasics.com>; from adampic@UBASICS.COM on Sun, Jun 03, 2001 at 11:22:48PM -0400
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Subject (change) ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")

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