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.

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- March 13th 2010, 04:24 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. - March 13th 2010, 04:41 PMDefunkt
First take , for example. if then .

Now take . If then , but so that is a contradiction.