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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 (w
by 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 agoYour 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 agoThe 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 agoDid I say it was a mathematical proof?