>>11468589In a sense it could but so does classical computers.
There is an algorithm that output an approximation of Pi with arbitrary precision in finite time, which means that Pi is what we call a "computable number". Essentially, you can use Pi in any algorithm as if you had the exact value and it will run exactly the same even through it's implemented using the approximation algorithm.
This works because "any algorithm" more precisely means "any computable task". At any point in time, all the information that the algorithm uses about Pi must be finite, and the approximation algorithm is able to provide that.
Another way to see it is that the "approximation algorithm" of Pi is just another one of its representations, the same way that although 0.333333... is infinite, it's just a different representation of the number 1/3, a.k.a. the finite pair (1, 3). That way its easy to see that because different representations don't "loose" information, if any of them (e.g. the approximation algorithm ) is finite, then it can be used in any computable task like the real thing.
That's the whole point of computable numbers btw. If a number has a finite representation, then it has an approximation algorithm with arbitrary precision and finite time. So this definition of computable numbers is just a convenient way of saying "any number that has a finite representation and therefore can be handled by computers".
So next time someone tells you "hurr durr you can't have Pi in your computer" you better make me proud anon
>>11468774See above
