piclist 2001\06\03\134459a >
Thread: ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")
www.piclist.com/techref/index.htm?key=brain+burp+rounding
BY : Sebastian Garcia email (remove spam text)

| Earlier in this thread, the most simple (IMO)) proof that
| 0.999(Repeating) = 1 was shown using no magic, mirrors or divides by 0.
|  There are 3 thirds in a whole (ie 3*(1/3) = 1)
|   and, 1/3 = 0.33333333(repeating forever) (divide it out and see!)
|     Multiply that by 3 and get 0.99999999(repeating forever) (try it!)
|     Therefore 1 = 0.99999999(repeating forever)
| It may be uncomfortable, but it is true!

Hi,

Leaving behind calculators and computers, mathematically "it can be proof"
(i'm not doing that in this post)that the following are two different
decimal series development for the same number:

1)    1

2)    0.99999999...  (infinite periodic digits)

A quick view: Starting with, for example, the number: 0.999 and "appending"
by steps a 9 to the rightmost digit, the number obtained step by step is
greater. You can find in every step infinite real numbers between  the
number obtained and 1. Remember that in the real set of numbers, there's
always an infinite quantity of numbers between two different numbers. This
is not what it happens in the limit, You can't find infinite (in fact, You
can't find *any* number...) real numbers between  0.999...  and 1.

So the mathematical proof of the equality is based on showing that between
0.9999... and 1 there's not an infinite quantity of real numbers.

Best regards,

S.-

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