The title of my last post "Almost Cauchy Sequence" made me wonder if "Almost Cauchy" was already defined in some formal sense. I could not find much on "Almost Cauchy" ... but I did find out about "Almost Convergence." (I think I have ran in to this before... but it is very neat... observe:)

A sequence is almost convergent to L if for any we can find an integer n such that the average of n or more consecutive terms in the sequence is within of L. Formally, (I took this definition from here, and I wonder why they didn't mention that we need or else we are looking at negative terms in the sequence... But, maybe there is an interpretation of something like ? Or maybe the author thinks that would be obvious? I'm going to ask at the mathematics stack exchange!)