I.4.6

6/5/2021

4.5 is stupid, so we're doing this instead. Sorry for the delay, folks, but reminder:
this section only has 10 exercises. So yeah, OHHHHHH WE'RE HALFWAY
THERE, OHHHHHHHH LIVIN' ON A PRAYER.

While I am less than halfway to becoming girl (male), I am successfully
unemployed (accidentally), as reader may be aware. Alas: The former is but a
pipe dream. So I shall turn my attention to the other trigger that's gotta be
pulled (See next post).

Also I'm unvaxxed and am trying to stay unvaxxed. Let's just say, my area doesn't like that very much.

This exercise takes like no effort, BTW.

(a_{0},a_{1},a_{2}) |
(a_{1}a_{2},a_{0}a_{2},a_{0}a_{1}) | ||

(a_{0}a_{2}a_{0}a_{1},a_{1}a_{2}a_{0}a_{1},a_{1}a_{2}a_{0}a_{2}) | |||

= (a_{0}^{2}a_{
1}a_{2},a_{0}a_{1}^{2}a_{
2},a_{0}a_{1}a_{2}^{2}) | |||

= a_{0}a_{1}a_{2}(a_{0},a_{1},a_{2}) | |||

= (a_{0},a_{1},a_{2}) | |||

So ϕ is its own inverse, and birationality follows from part (b)

Let U and V be the open set given by x≠0,y≠0,z≠0. Done.

Anywhere that isn't (1, 0, 0), (0, 1, 0), (0, 0, 1). Done.

Yeah, that's the whole exercise LOL. The only thing that makes it difficult is that
it's that whole stupid vague as "it's defined but it's NOT defined oooooo"
nonsense from 4.3b, so you have to read the exercise like "Hmmm, what did the
author mean by this?" Well, I checked my answers with the solution, and it looks
like I guessed right.