Mnementh said:
Fayceless said:
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.
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Bolded: no you can't. The numbers as we write themare constructs of math. We wrote symbols down and said they represent some sort of abstract concept of multiplicity. In this concept of writing down, different ways led to different representations. So, 1/3 can be written as 0.3333 (assuming the 3s go on infinite). But if you really have a infinite sequence of 9s after the decimal point, it gains basically a carry. Let's assume writing a infinite seuqence of 9s is correct: even in this case it is only a different representation for 1. But construct an mathematical operation, that produces 0.999... I can come up with 1/3 multiplied with 3. And that is 1, not 0.999...
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Okay, I do see your point.
But it's no fun. :P
It's fun to question things. Like math. And what things mean.
