3 ms·
> But “imaginary” numbers are no more or less legit than, say, transcendental numbers. I disagree? The ratio of a circumference to a diameter is clearly a posi
by dataflow 5y ago
> But “imaginary” numbers are no more or less legit than, say, transcendental numbers.
I disagree? The ratio of a circumference to a diameter is clearly a positive number between 3 and 4, and it sure feels more legit than something whose square is a negative number.
- openfuture 5y agoWell it's not that the square is a negative number but rather that you were only taught to do arithmetic with 1x1 matrices so you don't have a nice abstraction in your head to convince yourself. It's similar to people who insist that 0 is not a natural number because they haven't studied abstract algebra and don't care about the underlying algebraic structure (nevermind that peano arithmetic starts by postulating zero and succ...)
- ravi-delia 5y agoWhy would abstract algebra suggest 0 is a natural number? The natural numbers aren't so much as a group, with or without 0. Peano starts with 0 because it's easier that way, but starting with 1 is easier for other things.