Your reasoning is correct, so it means that integers are not definable inside "real arithmetic". http://en.wikipedia.org/wiki/Real-closed_field http://en.wikip

Your reasoning is correct, so it means that integers are not definable inside "real arithmetic". http://en.wikipedia.org/wiki/Real-closed_field http://en.wikipedia.org/wiki/Real-closed_field If you don't believe this, try writing down a formula in the language of this theory that says "x is an integer". Ultimately, the issue is that the first-order theory of real closed fields contains no axiom approaching the induction scheme of PA in power.