I invest x today which buys one output so tomorrow I can get double the output for which the value is y. If y < x...
Hold it. If
y is twice the value of
x, then, by definition,
y is
not less than
x (assuming positive values of
x and
y).
...(we both agree in nominal terms we have less money), then it is certainly better I not invest x in the first place because y = 2 output and x > y, thus x > 2 output.
Impossible.
x is
1 output, remember? How, then, can it be greater than
2 output? Oh, right, because you assumed that
y < x when the opposite is the case.

Consider 2 periods t=0 and t=T.
Those aren't 2 periods. Those are just three ways of writing the number zero.
0 is zero,
t is zero, and
T is zero.
Any any real positive value at time T will hold for time t=0 irregardless of the nominal value, wouldn't you say so? If I invested 10 at t=0 and get 8 at t=T and at t=T, 8 buys me 8 goods, wouldn't that 10, I spent at t=0, if saved and spent at t=T buy me 8 goods + more?
Uh, yeah. "Saving" 10 for a zero period of time is better than "investing" 10 and instantly receiving 8. Not exactly what I would call a good investment, though. Or a good savings, plan, for that matter. "Saving" and "investing" is generally something that you do for a non-zero period of time (at least, that's the way I do it). What was this supposed to prove, exactly?