My view on it is that *infinity has no end*, so there is no "end" to 0.999..., nor is there an end to 10×0.999...=9.999...

It is the peculiar nature of infinity. You see inifnity is not a big number! It is a concept that says "not finite", or simply "no end".

]]>Basicly what you're doing is the same, but it's easier to do it the other way around. You're welcome to prove me wrong though, I like learning

]]>We always take the shortcut to move the decimal place, but is that a proven method or just a shortcut. I suppose the fact that we are using a decimal system for our calculations would indicate that you may be able to, but I thought I'd just pose that as a question.

Now, I don't know if I'm just looking at this too simply or not, but that's just a thought.]]>

Another good proof is 1/3 = 0.333.... * 3 = 0.999.... but 1/3 * 3 = 1.

]]>If they go on forever, then there isn't a limit to them, which means that it's impossible for X to have one more 9 after the decimal point than 10X.

This has already been discussed at length here.

]]>The conjecture is that 0.9 recurring (i.e. 0.9999....9) is actually equal to 1

(For this exercise I will use the notation 0.999... as notation for 0.9 recurring,

the correct way would be to put a little dot above the 9)

Let X = 0.999...

Then 10X = 9.999...

Subtract X from each side to give us:

9X = 9.999... - X

but we know that X is 0.999..., so:

9X = 9.999... - 0.999...

or: 9X = 9

Divide both sides by 9:

X = 1

But hang on a moment I thought we said X was equal to 0.999...

Yes, it does, but from our calculations X is also equal to one. So:

X = 0.999... = 1

Therefore 0.999... = 1

Does anyone disagree with this? Let me know using the math is fun forum.

No, this is not true, properly following the initial equation set out we find that.

X=.999

10X=9.99

Yet,

9X=8.991, and not in fact 9.999, so following through X=8.991/9 being .999 so X conforms to the expected solution.