Fayceless on 29 April 2013
| Mnementh said: http://en.wikipedia.org/wiki/Limit_of_a_sequence Some here already said it right: the sequence of 9s is converging to 1. It would reach it, if the sequence is infinite, that what was meant. But in the end a infinite sequence of 9s after decimal point never occurs in correct calculation. You could write 1/3 in decimal form (actually you can't as it is an infinite sequence) and multiply it with 3. If you plain multiply each of the decimal numbers it seems, like the result wouldbe 0.999..., but in reality the carry you would have after infinite number of operation would make it 1. Really, the number 0.999... (if the sequence goes on infinite) doesn't exist. That doesn't break math as some here claim, math pretty good handle this. |
Math doesn't handle it, mathemeticians made rules to handle it. Math is our way of simplifying the world around us, and sometimes the world is more complex than a simple numerical representation can accurately reflect. Thus, for all practical purposes 0.999999.... does equal 1. But one can very well make a sound argument that the two are, in fact, not the same number. But that's a question of pure logic, not math, which is practical logic.
