NOTE- "BIRTH OF MATHEMATICS MUST BE NON MATHEMATICAL UNTIL MATHEMATICS IS BONE " ????
Therefor we can not have mathematical proof for foundation of mathematicians . Because mathematics is did not exist in the birth of foundation of mathematics
We can represent natural numbers as N={1,2,3,4 ............n } .. or S= {a,b,c ...........k} (just symbols no mathematical meaning ) There is no way to tells that N is the natural numbers until we define it . where definition is kind of none mathematical thing which can be use to give a birth mathematical terms .
" THEREFOR WE DID'NT HAVE MATHEMATICS BEFORE WE DEFINE IT "