How to write this in formal language

• May 13th 2011, 03:58 PM
ikurwae89
How to write this in formal language
The set of even natural numbers not expressible as the sum of two primes is finite.

How do you write even numbers in formal language? i'm talking about peanos first order.
• May 13th 2011, 04:13 PM
emakarov
n is even iff $\exists m\,(2m=n$)

n is expressible as the sum of two primes iff $\exists m_1\exists m_2\,(\mbox{prime}(m_1)\land \mbox{prime}(m_2)\land n = m_1+m_2)$

The set of natural numbers satisfying a property P is finite iff $\exists n\forall m\,(P(m)\to m

Try expanding prime(m).
• May 14th 2011, 03:58 PM
ikurwae89
im sorry what do u mean by expand?

do u mean write them in abberviations ?
• May 14th 2011, 04:07 PM
emakarov
I meant, try writing prime(m) in the language of Peano Arithmetic.
• May 21st 2011, 05:45 PM
ikurwae89
yeah it make sennse i got it :) thanks xD