0.999...= 1
There is no proof that will ever satisfy a person dead-set against this. Ever since I brought this home from school as a child, my whole family ribbed me mercilessly for it.<p>If you tell a person that 3/6 = 1/2, they'll believe you - because they have been taught from an early age that fractions can have multiple "representations" for the same underlying amount.<p>People mistakenly believe that decimal numbers don't have multiple representations - which, in a way is correct. The bar or dot or ... are there to plug a gap, allowing more values to be represented accurately than plain-old decimal numbers allow for. It has the side effect of introducing multiple representations - and even with this limitation, it doesn't cover everything - Pi can't be represented with an accurate number, for example.<p>But it also exposes a limitation in humans: We cannot imagine infinity. Some of us can abstract it away in useful ways, but for the rest of the world everything has an end.<p>I wonder if there's anything I can do with my children to prevent them from being bound by this mental limitation?