I have to prove the following, and while I understand why the following is true, and I am not sure how to begin writing it out(adsbygoogle = window.adsbygoogle || []).push({});

Let m.d1d2d3... and m'.d1'd2'd3' represent the same non-negative real number

1)If m<m', then I have to prove m'=m+1 and every di'=0 and di=0

2)If m=m' and there is such i that di does not equal di' then we let N=least element of {i/di does not equal di'}. If dN<dN' then dN'=dN + 1, di'=0 for all i>N, and di=9 for all i>N.

Once again, I understand why this is true simply because of the nature of 1=.9999... and therefore there being at most two decimal representations of any number, yet I am not sure how to go about proving such a statement.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Some theorems regarding decimal representations

**Physics Forums | Science Articles, Homework Help, Discussion**