$T$ is defined on $\mathbb{N} \times \mathbb{N}$ by $(a,b)\mathrel{T}(c,d)$ if and only if $a \leq c$ and $b \leq d$.

I know this is a partial order relation as it is Transitive, Anti Symmetric and Reflexive but I'm not sure if its total order relation and whether they are well order relations?

  • $\begingroup$ try compare $(1,2)$ and $(2,1)$. $\endgroup$ – Ofir Schnabel Apr 29 '15 at 8:12

It is not a total order: just compare $(1,0)$ and $(0,1)$. It is a well partial order, a result known as Dickson's lemma.

  • $\begingroup$ Im assuming a well order relation is different from a well partial order? As I don't think we have learnt Dickson's Lemma yet $\endgroup$ – Sunny Apr 29 '15 at 8:20
  • $\begingroup$ @Sunny. Look at the first sentence of this page on Well orders : In mathematics, a well-order relation (or well-ordering)... As a rule, please look at Wikipedia before asking any question on math.stackexchange. $\endgroup$ – J.-E. Pin Apr 29 '15 at 8:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.