Miff

I found out there are offical lyrics to the #yugioh dub themes on the offical YouTube channel and am disappointed to learn that the third line of Hyperdrive is "Do you think you can win? Only if I lose." and not "Do you think you can win only if I lose?" which fits the themes of 5D's a lot better.

I wonder if cohost legit changed their designs or if they haven't realized lie to everyone day is over

I'm trying to cut down on computer/tech related stuff in my life again.

Material nonimplication (aka "abjunction" or "implies not") is my favorite boolean operator because, while it's pretty much useless for electronics or computing, you can build a complete functioning circuit using NIMPLY logic, which I will now ramble about.

I'll be using ⥇ to represent the operation here since the Unicode symbol that looks closest to the mathematical one (U+219B) has some rendering issues on my machine.

First off, what the operator means is that A ⥇ B is true if and only if B is true but A is false. So it's essentially an odd AND. This also means it's not communitive like most boolean operators since swapping A and B get different results.

So with a constant B = 1, we can get NOT.

A ⥇ 1 ⇔ ¬A

Then since it's just an odd variant of AND, we can negate A to turn it into an actual AND.

(A ⥇ 1) ⥇ B ⇔ ¬A ⥇ B ⇔ A ∧ B

By inverting B instead of A, we get a NOR gate instead.

A ⥇ ¬B ⇔ A ⥇ (B ⥇ 1) ⇔ A ↓ B

Interestingly, the NIMPLY operator works great for defining XOR as "A OR B but not A AND B".

(A ∧ B) ⥇ (A ∨ B) ⇔ A ⊕ B

In summary:

NOT: ¬A ⇔ A ⥇ 1

OR: A ∨ B ⇔ (A ⥇ (B ⥇ 1)) ⥇ 1

NOR A ↓ B ⇔ A ⥇ (B ⥇ 1)

AND: A ∧ B ⇔ (A ⥇ 1) ⥇ B

NAND: A ↑ B ⇔ ((A ⥇ 1) ⥇ B) ⥇ 1

XOR: A ⊕ B ⇔ ((A ⥇ 1) ⥇ B) ⥇ ((A ⥇ (B ⥇ 1)) ⥇ 1)

XNOR: A ⊙ B ⇔ (((A ⥇ 1) ⥇ B) ⥇ ((A ⥇ (B ⥇ 1)) ⥇ 1)) ⥇ 1

In conclusion, it's likely I got some math wrong somewhere and TIL what the mathematical symbol for exclusive nor is.