4 ms·

Why do you think it's circular reasoning?

• umanwizard 9y ago
  Because 0.33... means 1/3 for exactly the same reason that 0.99.. means 1. So if you believe one then you should already believe the other. All the intuitive (wrong) arguments against 0.99...=1 apply to 0.33...=1/3 just as well.
  • cgmg 9y ago
    Your first sentence is probably true, but the point is that most people find the former more intuitive. It's a valid demonstration technique. Just because A entails B in the mathematical/logical sense doesn't mean everyone who believes A also believes B. No one is logically omniscient.
    • umanwizard 9y ago
      The point of mathematical proofs isn't really to convince people psychologically that something is true -- it's to show why something is true. Do you really know "why" 0.99.. = 1 by writing 0.99... = 3 * (0.33...) = 3 * 1/3 = 1 ? I'd argue that you just kicked the can down the road.
      • cgmg 9y ago
        Did I say it was a mathematical proof?