0.999... = 1

[Imagine]

Yes, but, 0.999 (with any finite number of 9's) over 1 is not 1/1.

Again, you're missing the point of my argument. I completely agree that any finite number of 9's is not the same number as one. I'm just arguing that with an infinite, and with an infinite number of 9's only, that .999... = 1.

Does the number line extend to infinity?

Well no, quite honestly it could extend from 0-1. You don't use a number line for the number of decimal places a number has, you are just able to place the number more precisely on the number line...

 

[malakadang]

Again, you're failing to miss the point of my argument. I completely agree that any finite number of 9's is not the same number as one. I'm just arguing that with an infinite, and with an infinite number of 9's only, that .999... = 1.

I agree with that, however since you've applied an abstract concept to it, you shouldn't be surprised with the contradiction in reality.

Well no, quite honestly it could extend from 0-1. You don't use a number line for the number of decimal places a number has, you are just able to place the number more precisely on the number line...

Can the number line extend to infinity (Is it possible if you wanted to draw the biggest number-line possible)?

 

[Annex]

While it is a good debate topic the only reason this actually exists is because fractions (and further more onto division) and our number systems don't interact correctly enough to produce a result that we can actually understand.