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? Wouldy= pi be a valid counterexample? Thanks in advance.

Printable View

- Mar 13th 2010, 03:24 PMbearej50False 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. - Mar 13th 2010, 03:41 PMDefunkt
First take $\displaystyle y_1 = -1$, for example. if $\displaystyle x = y_1+1$ then $\displaystyle x = 0$.

Now take $\displaystyle y_2 = 0$. If $\displaystyle x = y_2+1$ then $\displaystyle x=1$, but $\displaystyle x=0$ so that is a contradiction.