/sci/ - Science & Math

>>12105107
You only need to show that
((P -> ⊥) -> P
<=>
((P -> ⊥) -> ⊥

The <= direction is true by concatenation with explosion.
The other direction - I don't know the details of your setup, probably follow from considering that your assumption also holds true for P=bot and bot->bit holds

I got a PhD in physics theory and of the 15 or so people who graduated in my semester, most are at banks, consulting or energy companies. Two are at CERN, one is at a similar institution. I'm probably the only one not doing HEP but something physics related, and e.g. a year ago I was writing Kalman filters.

>>11623879
btw. you generally have nice handwriting

>>11566839
You can see it as an abstraction from arithmetic, where a false statement (say [math]5^2=16[/math]) enables one to proof anything.
Consider how [math]0=1[/math] implies e.g. [math]4=4+0+0+0=4+1+1+1=7[/math].

Practically speaking, in propositional logic, this rule (explosion) is one means to argue for the Disjunctive syllogism
[math] ((A\lor B)\land \neg A) \to B [/math]

See
https://youtu.be/eeLa9tIhFMs

>>11554954
Yeah, we're already eating out of the trash can of set theory all the time.