Thread: Can anyone help me with this proof?

Give a complete, formal proof of the following statement: If

a 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!

Originally Posted by Nappy

Give a complete, formal proof of the following statement: If

a 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!

Maybe my question is dumb: Why can't we just take ?

Originally Posted by Nappy

Give a complete, formal proof of the following statement: If a 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.

Clearly if then works.
So suppose that then .
Using the Archimedean property, we know .
You finish.