3 ms·

To your main point: are irrational numbers, say, "out there"? If so, where? On the sheet of paper in front of me, as the hypotenuse of the isosceles right-angl

• pbhjpbhj 15y ago
  >as the hypotenuse of the isosceles right-angled triangle with unit length I drew a moment ago // Doesn't the quantised nature of matter mean that 2^½ exists as a real measure of a material object only as much as a perfect circle actually is existent in our universe?
• jberryman 15y ago
  > Irrational numbers are probably a bad example of what you're talking about. No, they're the perfect example and you're observation about the unit square is glib. Trying to reason about the diagonal of the unit square basically destroyed the Pythagorean world view of integers as the fundamental building blocks of reality. If mathematical entities are simply discovered and that-is-that, then why did it take nearly two millenia after this observation for western math to accept irrationals as numbers? From M. Stifel, 1544: "Now, that cannot be called a true number which is of such a nature that it lacks precision. Therefore, just as an infinite number is not a number, so an irrational number is not a true number, but lies hidden in a kind of cloud of infinity"