## How would I write a proof for this partial order and total?

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

### How would I write a proof for this partial order and total?

Let R1 and R2 be relations on N defined by
xR1y if and only if y=a+x for some a in N0.
xR2y if and only if y=xa for some a in N.
for all x,y in N.
Also N0 denotes all integers x>=0, while N denotes all integers >= 1.

There are two different things I want to write a proof for with this.

1.
I want to write a proof to show that R1 is a total order on N.

2.
I want to write a proof to show that R2 is a partial order on N.

I have others I want to try and do but for now if someone could model how to do
the first one and then I can use your proof to complete my second.
hn3032

Posts: 1
Joined: Tue Dec 10, 2013 3:34 am

hn3032 wrote:Let R1 and R2 be relations on N defined by
xR1y if and only if y=a+x for some a in N0 = {0, 1, 2, 3, ...}
xR2y if and only if y=xa for some a in N = {1, 2, 3, 4, ...}
for all x,y in N.

1. Show that R1 is a total order on N.

2. Show that R2 is a partial order on N.

What definitions have you been given for "partial" and "total" orders? Thank you!

stapel_eliz

Posts: 1799
Joined: Mon Dec 08, 2008 4:22 pm