Tragedy has bestruck this blog again. 3 months following the Murray-holeinmyheart incident, I have now had to make my second redaction. Yes, it's Redacted 2: Electric Boogaloo. I made another cringe post. And now Neil Gaiman is joining Bill Murray in the DEATH PILE. Bill Murray: SLAIN. Neil Gaiman: SLAIN. Who's next? Was it worth it? Was it worth the 6 million more readers we lost? Here we are, standing on a pile of 6+6=12 million dead readers. Look into my eyes, holeinmyheart. Was it really worth it? All just for revenge? Just to get the last laugh against Mr. Gaiman? Do you feel happy? Are you happy? Look into my eyes and tell me you're happy. No, no. Don't look into my eyes. *Picks up the body of a dead reader; a femboy with his tongue sticking out in a sort of lifeless ahegao... the Final Orgasm* Look into HIS eyes. Look into dead eyes and tell HIM you're happy. Or how about this one? *Picks up the dead body of another reader–a poor little brush rabbit, yes, cute rabbits read this blog. It's accessible to all species* Look into HIS eyes and tell him you're happy. Can you do it? Answer me, holeinmyheart. Can you do it? CAN YOU? WAS IT WORTH IT? WAS IT FUCKING WORTH IT, YOU SICK BASTARD! ARRRGGGGH *SLAP, SLAP* ARRRRRGGGGH,,, YOU KILLED MY FAMILYYYYYYYYYY.... YOU BASTARRRRRRD.... MY WHOLE FAMILY READS THIS BLOG AND YOU KILLED THEM WITH YOUR CRINGY POST,,,, ARRGGGHHH *STRANGLE* ....... YOU FUCKING BASTARDDDDDDD. YOU KILLED THEMMMM....... MY DAD, MY MOM, MY POOR LITTLE SIS... SHE WAS ONLY 5 AND YOU KILLED HERRRRRRRR.... HOW IS YOUR WRITING SO BAD THAT IT LITERALLY KILLS PEOPLE...

It's okay they'll just get counted as covid deaths LOLOLOLOLOL I have a list here of some of the fallen readers of this blog: Rainbow Dash, Pinkie Pie, Twilight Sparkle, Lee Goldson, TK-47, Sakurafish (extra rip), the boymoder poster, Juan Ovus (your sacrifice will never be forgotten. Just remember that although Ovyu wasn't your biological brother, he still loved you), Kilim, Ronald McDonald, his sociopathic friend... The list keeps going. And they're only some of the 6 million we lost. Many of them are nameless anons, just like (You). Now, everyone, kneel. #KneelForNeil Kneel for the lost souls.





"Ummmm, was it that bad?" Errrr, not as bad as 3.16 (that one only took an hour to be beaten off the face of this blog), but bad enough. OK: although redacted, I did in fact complete a,b,c (and this time I do have a copy of it, in case I ever need to look back at the math part, LOL). So let's finish the job. Here we are, baby: Part D.

D

So... the thing is, I can do this exercise. Just watch. The "Q′" they're looking for is obviously Q′ = Z(f) (it's just f in k[x₀,…,x_r] instead of k[x₀,…x_n]. Now, let's say P = (p₀,…,p_r) ∈ Q and S = (s₀,…,s_r,s_r+1,…,s_n) ∈ Z (and we know s₀,…,s_r = 0). So if I embed P^r in Pⁿ like they describe. Then I'm sending

(x0,…,xr)

(x0,…,xr, 0, 0,…, 0)

(so clearly P^r ∩ Z = ∅, as needed). So where does P get sent to? P gets sent to (p₀,…,p_r, 0, 0,…, 0), right? So we have

P	= (p0,…,pr, 0,…, 0)
S	= (0,…, 0,sr+1,…,sn)0

Now, we are going to connect P and S with a line. Now, if you did read yesterday's awful post, you'll know that I don't know how to do this in projective space. However, let's take the "common sense" route and connect them parametrically as if they were in affine space. The "line" between the two is the set of points L = (l₀,…,l_n), where

l0	= s0 + (p0 - s0)t
ln	= sn + (pn - sn)t

Plugging in the 0s, we get

l0	= p0t
lr	= prt
lr+1	= sr+1(1 - t)
ln	= sn(1 - t)

where t ∈ k is a scalar. Now keep in mind that there are no restrictions on s_r+1,…,s_n are free, which means, according to the equations above, l_r+1,…,l_n are also FREE. So I can get rid of those equations entirely. Now we are left with

l0	= p0t
lr	= prt

But WAIT: This set of equations say that l₀,…,l_r merely have the same restrictions as p₀,…,p_r. I.e. f(l₀,…,l_r) = 0. I.e. f(l₀,…,l_n) = 0.

The only problem is that I used the parametric representation of a line, which is not how we defined "lines" in the context of varieties. A line in projective space is a linear variety–the zero set of a set of linear homogenous polynomials. I still don't know how to construct that. I know it's equivalent to the parametric representation BUT AAAAAAAAAAAAA.