Originally Posted by

**kurac** Im doing some self study and I would like to ask question about linear orders.

Listing all linear orders (total orders) of the set {a,b,c}:

Is that just: (a,a) < (a,b) < (a,c) < (b,a) < (b,b) < (b,c) < (c,a) < (c,b) < (c,c). Is this correct? There is another way shown in my textbook,but i think this is the correct way.

Also, how many ways can one linear order a set with n elements?

I was thinking it would n x n different ways, because in above example with 3 elements i ordered it 9 times? I dont know how to prove this (im very bad at proofs!!!)

Does anyone know how to explain this with a small simple proof or explanation?

Much appreciated, Kurac.