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.
The thing that really got 0.999…=1 to click on my mind is the fact that you can’t find a number between 0.999… and 1. You might think “Just put something at the end of 0.999…,” but there is no end to 0.999…
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.
