Question:(adsbygoogle = window.adsbygoogle || []).push({});

Decimal (10-nary) expansions of real numbers were defined by special reference to the number 10. Show that the real numbers haveb-nary expansions with analogous properties, wherebis any integer greater than 1.

Attempt at solution:

I think if I show that there is a bijective function between the real numbers base ten, and any other base that will show they have analogous properties.

so let a_{0}.a_{1}a_{2}... be any real number, where a_{0}is any integer and a_{i}i >0 and i /in {0,1,2,...,9}.

Then it has been shown (in the book) that this can be represented as

a_{0}+ a_{1}/10 + a_{2}/10^{2}+ ...

I think now I need to show that this number can be changed into basebwhich I am not quite sure how to do. And even once I have done that, I am not sure that I am any closer to solving the problem.

Any help is appreciated.

Thanks

-Dif

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

Dismiss Notice

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!

# Base 10 and Base b

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