Is math something humans invented to make sense of the universe, or is math the actual bedrock of reality that exists completely independent of human minds?
Replying to @WahFo@meow.social
@WahFo Yes. π
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.
Replying to @tknarr@mstdn.social
@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
Replying to @SmartmanApps@dotnet.social
@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.
Replying to @tknarr@mstdn.social
@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.