The student's acceptance or rejection of 0.999 =1

[pwsnafu]

The point that I try to make is that a limit is NOT equality. A limit is a number that will not be reached and will not go beyond, because one can always add an iteration to the sequence. The fact that limits have been used so much to achieve success, doesn't mean that they are EQUAL. We also treat pi and e as if they were not limits, but numbers, nice habit, but not accurate.

Completely and utterly wrong. Each sentence is wrong. coolul007 you need to go back and study limits again, from the very beginning.

 

[Mark44]

A limit is a number that will not be reached and will not go beyond, because one can always add an iteration to the sequence.

I think that you have a fundamental misunderstanding of what a limit actually means, based on what you are saying above, particularly the part about "that will not be reached".

There is a big difference between saying a_n = L and $\lim_{n \to \infty} a_n = L$, and you seem to not be getting that difference.

 

[micromass]

The point that I try to make is that a limit is NOT equality. A limit is a number that will not be reached and will not go beyond, because one can always add an iteration to the sequence. The fact that limits have been used so much to achieve success, doesn't mean that they are EQUAL. We also treat pi and e as if they were not limits, but numbers, nice habit, but not accurate.

There is little point in continuing this discussion. I do understand that you think that 0.999... is not equal to 1. I even understand why you think that. The problem is that you seem to be missing quite some basic knowledge about real numbers. Without this knowledge, I think it would be impossible to fully grasp the 1=0.9999... situation.

So, if you're truly interested in understanding the equality 1=0.9999..., then I can only suggest you to start studying limits and real numbers. Any good analysis book should cover these things very well. So please, do yourself a favor and try to study these things from the very beginning.

I'll keep this thread open to see if we can get further discussion. But if people keep commenting without taking the effort of studying limits and real numbers, then we will be forced to lock.