>real number [math]r[/math] is represented by the sequence [math]r_1,r_2,\ldots[/math] of natural numbers continued fraction expansion
>convergence and limits are defined using this sequence
>addition is pointwise
>mult is discrete convolution ie, [math]r\cdot t = (\sum_{i+j=k} r_it_j)_k[/math]
>division is analogoous to inverse fourier transform