Thread: Concept of Quantity

Originally Posted by EVOEx

But at the very least, even if you take another definition, to me this seems to prove that there is no number between "0.9999..." and 1: if there were, the limit there would be less than 1!
And one can always find a number between two numbers that aren't equal: their average, for example.

Going on this logic, as said in an earlier post, then you have to consider that

Code:

lim(x->inf)(9*10^-x) = 0

so you are not getting closer and closer since you will be adding zero. True?
In other words the difference will always be "0.00..001". The more 9s you add the more 0s you can add and you are always on the same point.
And the logic you are getting closer and closer is controversial to infinity. If you have infinite space, will you ever reach the end? That is the point, you would never reach the end.
Even worse, if you can reach 1, then if you add another 9s what happens? If you add another and another? Makes no real sense.
Wouldn't you agree that if there is no limit then it will grow bigger and bigger? If there is a limit that would be one, but by definition it will never reach it.