This little guy craves the light of knowledge and wants to know why 0.999… = 1. He wants rigour, but he does accept proofs starting with any sort of premise.
Enlighten him.
Yeah that’s something that people have to get used to in maths, if the limit of a sequence exists we can just pretend to have “reached infinity” and work with like any number
I’m not sure what you are trying to say here, and I have a background in math. I think this is just going to confuse lay people.
Im trying to make the distinction between a function that approaches a value as it’s input grows, for instance a sequence seen as a function on the domain of the natural numbers, and the value itself.
I have seen a lot of people view 0.999… as a number that “approaches one”, so formally speaking as the sequence (0.9, 0.99, 0.999, …) and not the number itself which that sequence approaches which they would agree is 1.
The “its the largest number which is less than 1” type of thinking.
I am going to note that this was not well-expressed when you said ‘we can just pretend to have “reached infinity” and work with like any number’. To a lay person it would look as if you were suggesting that we non-rigorously treat one object (like the sequence (0.9, 0.99, 0.999,…)) as another (like the real number that that sequence converges to given the standard topology of the space of real numbers).
I’m not really confused about what you’re saying here exactly, and since the original post is deleted, I can’t really even see what was originally said, but I was confused about this:
(like the real number that that sequence converges to given the standard topology of the space of real numbers).
Why make mention of the standard topology here exactly? It’s not exactly clear to me why this has anything to do with what you two are discussing.
