(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I was trying to prove trichotomy for natural numbers.

2. Relevant equations

[itex]n > m \Leftrightarrow \exists k \neq 0 (n = m + k)[/itex]

[itex]n < m \Leftrightarrow \exists k \neq 0 (m = n + k)[/itex]

Trichotomy means in a set

[itex] \forall n \forall m ( n = m \vee n> m \vee n<m) [/itex]

3. The attempt at a solution

I need an hint, a push in the right direction.

thank you :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Trichotomy proof

**Physics Forums | Science Articles, Homework Help, Discussion**