# Thread: Prove that R is a total ordering relation on A

1. ## Prove that R is a total ordering relation on A

I just want to apologize in advance for just posting the question. I'm sick as a dog, running a temp and can't even figure out what i'm reading and need this done by tomorrow so i'm sorry for not writing any of my ideas with it.

Let A be the set of all infinite sequences of nonnegative integers y = (y_1,y_2,...) having
the property that only a finite number of terms are nonzero. Define the relation R on A by xRy if there is a positive integer n such that x_n <y_n and for all i>n,x_i =y_i.
(a) Prove that R is a total ordering relation on A.

(b) Prove that for each positive integer n there is a section of A that has the same order type as (Z+)n with the dictionary order.

(c) Prove that A with the given ordering ia a well-ordering.

2. Originally Posted by alice8675309 I just want to apologize in advance for just posting the question. I'm sick as a dog, running a temp and can't even figure out what i'm reading and need this done by tomorrow so i'm sorry for not writing any of my ideas with it.

Let A be the set of all infinite sequences of nonnegative integers y = (y_1,y_2,...) having
the property that only a finite number of terms are nonzero. Define the relation R on A by xRy if there is a positive integer n such that x_n <y_n and for all i>n,x_i =y_i.
(a) Prove that R is a total ordering relation on A.

(b) Prove that for each positive integer n there is a section of A that has the same order type as (Z+)n with the dictionary order.

(c) Prove that A with the given ordering ia a well-ordering.
What've you done so far? Where're you stuck? the firtst part (a) only requires from you to REALLY understand the definition of R....what with it?

Being sick and needing this for tomorrow is no explanation, imo. Are you asking us to do your homework for you?

Tonio

3. Being sick and needing this for tomorrow is no explanation, imo. Are you asking us to do your homework for you?
Wow, no I wasn't actually I was pretty sick and couldn't get my thinking started (hence why i apologized for just posting the question because I didn't have scratch work because I wasn't making sense) but wow just wow.

4. Originally Posted by tonio What've you done so far? Where're you stuck? the firtst part (a) only requires from you to REALLY understand the definition of R....what with it?

Being sick and needing this for tomorrow is no explanation, imo. Are you asking us to do your homework for you?

Tonio
Again, i'm sorry for just posting the question. But I think what I'm having trouble with is (b) the section and the dictionary order. But then for part (c) can't i say that if it is the same type as a dictionary type then it is well-ordered (because of the property)?

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