@WahFo Yes.

@WahFo Yes. 😁

Consider that the integer arithmetic computers use isn't the integer arithmetic we use. Nor is FP arithmetic the same as the real-number arithmetic we're used to. And you can frame formal logic as a mathematical system with some really interesting properties distinct from normal math.

@tknarr @WahFo
"Consider that the integer arithmetic computers use isn't the integer arithmetic we use" - yes it is, it's just using a different base. 1+1=10 in base 2, and 2 in every other base, but in every case 1 thing plus 1 thing gives us two things, we just write it differently in different bases

@SmartmanApps @WahFo It's not the base that's different, it's the set of integers themselves. If you take the largest representable integer on a computer and add 1 to it, it wraps around to give you the smallest representable integer. In normal integer arithmetic there isn't a largest integer (or a smallest), the set of integers is infinite.

There are also arithmetics on a finite domain where adding 1 to the largest integer doesn't wrap around, it simply isn't defined.

@tknarr @SmartmanApps @WahFo I highly recommend reading a few of this guy's #MathsMonday pinned threads to get an idea of the extent of his mathematical understanding, and the chances you have of convincing him of anything. The ones about 0.999... are particularly illuminating.

@WahFo @tknarr

Maths is discovered, to be sure. But it's also invented in a way that is more significant than mere notation: the act of doing mathematical research *feels* like invention.

You don't just discover what's already there; you have to make the definitions and proofs yourself. The two points of view focus on different aspects of maths which both exist.