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"But the reals? Well they are invented purely so we can take the square root of two. " To follow on you previous run: ... because we can cut things into piece
by jVinc 8y ago
"But the reals? Well they are invented purely so we can take the square root of two. "
To follow on you previous run:
... because we can cut things into pieces and count the pieces. We know real numbers are real because we can cut a square across the diagonal and see the relative length of the diagonal to the side.
- pauljurczak 8y agoWe can't cut the square, because perfect square is an abstraction and what you are cutting is an approximation of the square. We can't cut across the diagonal, because all cuts are only an approximation of a straight line. We can't directly see the real number being the ratio of square diagonal to its side, because our eyes have finite number of photoreceptors, receiving information from a finite number of photons. It's natural numbers, all the way down...