When I was in pre-calculus, there was a 10-Day Pre-Cal syllabus. One of the days was, “Show them the video of the student factoring x^2 + y^2 = (x+y)^2 and getting HIT BY A TRAIN” so that made me laugh a lot!
It works for boolean algebra too, though admittedly I’ve never seen exponents used to represent iterated AND gates. That would be a seriously cute notational convention.
Sorry if this is a silly question, but shouldn’t it be foils powers, rather than foils products? Of course a power just indicates products, but the distributive rule works for products by one term.
When I was in pre-calculus, there was a 10-Day Pre-Cal syllabus. One of the days was, “Show them the video of the student factoring x^2 + y^2 = (x+y)^2 and getting HIT BY A TRAIN” so that made me laugh a lot!
Alas! Would that the world were a commutative ring of characteristic 2…
But my computer says:
sage: R. = GF(2)[]
sage: (x+y)^2
x^2 + y^2
;)
Okay, this comic goes on my office door. (Of course, that is why Z_2 is so nice.)
Oh, I just saw Jim Vaught’s comment. He already got the commutative ring of characteristic 2. Foiled again.
mod 2 and it works fine
We call this the freshman dream.
I only came here to suggest trying it in Z_2, but since you beat me to it, I could point out that it also works in Z_1 …
Another one: anticommutative rings!
It works for boolean algebra too, though admittedly I’ve never seen exponents used to represent iterated AND gates. That would be a seriously cute notational convention.
I’m a math tutor at a college campus…I’m definitely going to hang this up in the room. Printed out very large.
Doesn’t every equation work in Z_1?
well
this is funny….but also stupid mistake
It works in any Z_p. (x+y)^p == x^p+y^p (p)
(x + y)^2 = x^2 + y^2 is valid if xy + yx = 0.
Sorry if this is a silly question, but shouldn’t it be foils powers, rather than foils products? Of course a power just indicates products, but the distributive rule works for products by one term.