1,9999.... can only be the same (or equal) to 2 in some kind of imaginary world. The number 1,999... where there is an infinity of 9's does not "exist" in so far as it cannot be "represented" in a finite amount of space or time. The only way out is to "represent" infinity by (...). So you represent something infinite by something finite, thus avoiding a serious problem. But then stating that 1,999... is equal to 2 becomes a tautology.
Of course mathematicians now are used to deal with infinities. They can manipulate them any which way they want. But in the end, infinity has no equivalent in the "real" world. It is... (read more)
Benoit,
1,9999.... can only be the same (or equal) to 2 in some kind of imaginary world. The number 1,999... where there is an infinity of 9's does not "exist" in so far as it cannot be "represented" in a finite amount of space or time. The only way out is to "represent" infinity by (...). So you represent something infinite by something finite, thus avoiding a serious problem. But then stating that 1,999... is equal to 2 becomes a tautology.
Of course mathematicians now are used to deal with infinities. They can manipulate them any which way they want. But in the end, infinity has no equivalent in the "real" world. It is... (read more)