Math Help - False statement about the existence of a number

1. False statement about the existence of a number

There exists a number, x, that is a real number such that for all real numbers, y, x = y + 1

I know that this statement is false, but why? Would y = pi be a valid counterexample? Thanks in advance.

2. First take $y_1 = -1$, for example. if $x = y_1+1$ then $x = 0$.
Now take $y_2 = 0$. If $x = y_2+1$ then $x=1$, but $x=0$ so that is a contradiction.