Annnnnnd, it's the last exercise of this section. Or the last nonstarred exercise, since I'm skipping the starred ones. Yes, a month or two late, but HERE WE ARE. The BIG, EPIC END OF section 1!!!

Well, okay, I skipped 1.7d, 1.10c, and 1.10e. But hey, you know what. I think I need to move on to section 2. I've been spending way too much time on this. MAYBE I'll revisit these missed spots later. They can be "extras". Like OVAs, perhaps.

So consider this to be the SEASON FINALE. 12 exercises? Hey, it's just the right amount for a single cour (except there were actually 15 posts in total). Here we are, fellows. Thank you. THANK YOU TO ALL MY FANS, FOR STICKING WITH ME THROUGH THIS RIDE! *Wipes tear from eye, camera pans to show empty stage*.

But we're not done yet. We still have a lot of sections ahead of us. Heck, we still have to finish this challenging looking exercise. So, let's finish this section strong. NOW TELL ME: ARE YOU READY TO RUMBLE?

"Yea!"

Come on, I can't hear you!

"YEA!"

Louder!

"YEAAAAA!"

STILL CAN'T HEAR YOU. COME ON.

"YEEEEEEEEEEEEEEEEEEEEEEEAAAAAAA"

ONE MORE TIME. AS LOUD AS YOU CAN. ARRRRRRRRRRRRRRRE YOUUUUUUUUUUUUUUUUUUUUUUUUUU READDDDDDDDDDDDDDDDDAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYYYYYYYYYYYYYYYY TOOOOOOO RUMBBBBBBBBBBBBBBBBBBBBBBBLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLE

"YEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!"

ALRIGHT. LET'S DO THIS. SO THE EXERCISE SAYS "CF. 1.4.2" RIGHT?

"YES"

OKAY, NOW IF I ACTUALLY LOOK AT 1.4.2, IT DOESN'T SEEM THAT HELPFUL:

"I GUESS NOT"

BUT I SCROLL DOWN A BIT AND SEE THIS:

"OH, IT SAYS 'SEE ALSO (EX. 1.12)'"

YES. f = x² + y² + 1 IS AN IRREDUCIBLE POLYNOMIAL IN R, AND IT STRAIGHT UP TELLS US THAT ITS ZERO SET IN A_R² IS THE EMPTY SET.

"UH HUH"

BUT BY DEFINITION, THE EMPTY SET IS NOT IRREDUCIBLE:

"YEAH"

SO WE'RE DONE.


".............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................."

"YOU DID LIKE NO WORK, YOU FUCK. YOU JUST USED AN EXAMPLE FROM THE BOOK. WHAT WAS ALL THAT HYPE FOR?"

Uhhhhh.

"COULDN'T YOU AT LEAST COME UP WITH YOUR OWN EXAMPLE, THAT DOESN'T TURN OUT TO BE AS LAME AS THE EMPTY SET?

Well, it would be cool if I could do that, but I'm not that creative... That's why I skipped 1.10c and 1.10d.

".........."

...WELL, THAT'S ALL FOR THIS SECTION. SEE YOU IN SECTION 2!