Thursday, February 17, 2011

Limit over an interval

We are analyzing several FTC proofs to gain some insights. For now it seems all of them need analysis to be stated with enough detail to be convincing.
In this proof, I stumbled upon an assumption that can be reduced to claiming that this statement is true:

As usual, this is intuitively very true, the interval vanishes, leaving the 'sup' to act on only 'one point' if f is continuous. But that is no proof.

I have tried to detail this a bit more to see if I can prove it, the main idea behind my proof is: Courage.
I have found courage to be an essential component across many proofs and bold inventions in mathematics.
I am not sure how good it is, it feels pretty convincing, but there are 2 spots where it needs more detail, and I suspect that for these spots, there is an inescapable need for analysis (luckily we will be tackling that in the foreseeable future).


No comments: