Describe an algorithm for adding two infinite decimals. You should work from $$left to right$,$

determining the decimal expansion in order, as much as possible. When are you assured that

you know the integer part of the sum? In what circumstance does it remain ambiguous?

HINT: Given infinite decimals a and b$,$ define a carry function $\backslash$gamma : $\{0\}\backslash$cup N $->\{0,1\}$ and then

define the decimal expansion of a$+$b in terms of a$($n$)+$b$($n$)+\backslash$gamma $($n$).$