SGD: It's like getting a flat tire and fixing the problem by driving around the block a few times; maybe it will fix itself.

*The utility of Cauchy sequences lies in the fact that in a complete metric space (one where all such sequences are known to converge to a limit), the criterion for convergence*

**depends only on the terms of the sequence itself, as opposed to the definition of convergence, which uses the limit value as well**as the terms. This is often exploited in algorithms, both theoretical and applied, where an iterative process can be shown relatively easily to produce a Cauchy sequence, consisting of the iterates, thus fulfilling a logical condition, such as termination.I repeat for our CS friends and partners.

*convergence*

**depends only on the terms of the sequence itself, as opposed to the definition of convergence, which uses the limit value as well**as the terms.*And since we work in a*

**complete**RKHS space, it's bingo.