## 117b- Homework 6

Due Thursday, February 22 at 1pm.

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### 4 Responses to “117b- Homework 6”

1. Jed Says:

For #3, < respects + probably should read
x < y -> x + z < y + z
instead. Just a minor detail.

(Edited)

2. Jed Says:

A few more concerns:

1) x < y iff there is z such that x + z = y:
We are either defining \leq or we want z \neq 0. Of course we can define < this way, but it is just a bit more confusing. Judging from the statement 0 < 1 < x and also the definition of prime(x), however, I think we want < to signify strict inequality. But I could be wrong.

2) The hint tells us to show a model of PA. I think we want a model of PA-.

3. andrescaicedo Says:

Hi, Jed.
Yes, you are right about #3, all the things you point out are typos. Thanks for spotting them, and sorry about that.

So, yes, “x less than y implies x+z less than y +z”,
“x less than y iff there is z *different from 0* such that x+z less than y+z”, and
in the hint, it should read PA- instead of PA.

*Sigh*

4. Domenic Says:

Just think of it as demonstrating the superiority of the blog format for classes ;). In a normal class, there’d have to be several emails back and forth before the professor notifies the students via the website that there is an error in the problem set, whereas here we get instant feedback.