We give a new approach to the question of whether or not all greater than one, integer arguments of Zeta are irrational. Currently only Zeta(2n) and Zeta(3) are known to be irrational. We show that using the denominators of the terms of Zeta(n)-1=z_n as decimal bases gives all rational numbers in (0,1) as single decimals, property one. We also show the partial sums of z_n are not given by such single digits so using the denominators of the partial sum's terms as number bases, property two. Next, using integrals for the p-series contracting upper and lower bounds for partial sum remainders of z_n are generated. Assuming z_n is rational, it is expressible as a single decimal using the denominator of a term of z_n (property one) and eventually these bounds will consist of infinite decimals (property two) with their first decimal equal to this single decimal. But as no single decimal can be between two infinite decimals with the same first digit a contradiction is derived and all z_n are proven irrational.