Biggest number

There is an upper limit to numbers. Such that when yu add 1 to it you return to zero.

You may thing this is ridculous but this has far fewer paradoxes than the concept of "infinity".

x := biggest number, ie. there does not exist y such that y > x

then spse. x+1 = 0 (as you stated above)
=> (x + 1) - 1 = 0 - 1
=> x = -1

Consider y = 0.  I think you just failed.