This actually seems too complicated. If e = a/b, then if we multiply by b! then the right side is an integer, while the left side is an integer plus a fractiona

This actually seems too complicated. If e = a/b, then if we multiply by b! then the right side is an integer, while the left side is an integer plus a fractional tail 0 < 1/(b+1)+1/(b+1)(b+2)+... < sum{1/(b+1)^n} = 1/b.