Give a complete, formal proof of the following statement: Ifa is an element of the real numbers, then there exists a negative

integer n such that n < a.

I know its related to the archimedean property but cant find the proof anywhere.

Cheers!

Printable View

- Aug 11th 2010, 11:44 AMNappyCan anyone help me with this proof?Give a complete, formal proof of the following statement: Ifa is an element of the real numbers, then there exists a negative

integer n such that n < a.

I know its related to the archimedean property but cant find the proof anywhere.

Cheers! - Aug 11th 2010, 11:58 AMundefined
- Aug 11th 2010, 12:01 PMPlato
Clearly if $\displaystyle a\ge 0$ then $\displaystyle -1<a$ works.

So suppose that $\displaystyle a<0$ then $\displaystyle 0<-a$.

Using the Archimedean property, we know $\displaystyle \left( {\exists N \in \mathbb{Z}^ + } \right)\left[ { - a < N} \right] $.

You finish.