# 0.999...=1 project

1. Mar 18, 2005

### chickenguy

Need urgent help

sorrypeople if this annoys u but please don't close this thread. i need urhent help with my 0.999...=1 project and i have a new thing my teacher told me would help, but i don't understand!!!!!!!!!!!!!!!!!!
0.9=1- 1/10(fraction)
0.99=1-1/100(fraction)
0.999=1- 1/1000(fraction)
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1-(approaches zero)=1

sequence and series.
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Also, any background information and/or history and/or opinions and/or information would be very greatly appreciated!!!!!!!!!!!!!!!!!!!!!!!1

2. Mar 18, 2005

### matt grime

OPinions are not required. The real numbers are by construction somewhere where convergent sequences of rationals have unique limits. the sequence 0.99..9 with n nines converges to 1, that is what the above states - the distance from it to 1 is 10^{-n} which converges to zero.

so 0.999... the infinite string of nines which, by definition also represents the limit of that sequence mustbe equal to one by fiat.

3. Mar 24, 2005

### joeboo

Let x = 0.999999...
10x = 9.999...=9+0.999...=9+x
10x - x = 9
9x = 9
x=1

0.999... = 1