Thread: Concept of Quantity

Originally Posted by C_ntua

Yes, but you are adding every time a smaller amount. So in the end you are adding something very close to 0. Which in the case of a truly infinite amount of 9s that will imply that you are actually adding 0 thus you will never get to 1. In other words the amount you are adding can get closer and closer to 0 and in the limiting case it will equal to 0.

Very close, yes, but never equal. When dealing with limits, the difference (epsilon) approaches but never equals 0. If it does, the limit is undefined.

There is no "limiting case," you simply add increasingly smaller amounts forever.

This was an interesting thread, but I have to say there is quite a bit of confusion involving limits and their definition and rationale, especially about the "epsilon," or what some have been calling the "infintesimal." E > 0 always. NOT 0.

Some would be better served reading a calculus textbook (limits and infinite series) than attempting to disprove the calculus. I guess the problem is one of viewpoint; whether or not a (finite) limit produces a single, unique real number or not, and whether this number cannot be used like any other real number for some strange reason.

In other words, its a debate about the validity of the definition of a (finite) limit whether or not 0.999... = 1.

Overall, I have to say that reading this thread has not convinced me that the definition of a limit is flawed.