Yes. Despite this apparently popular saying, "close enough" is sufficient in almost everything in life. Usually it's the best you can get anyway - and this is fine, because on most things, you can also iterate, and then the only thing that matters is that you keep getting closer (fast enough to converge in reasonable time, anyway).

Where "close" does not count, it suggests there's some artificial threshold at play. Some are unavoidable, some might be desirable to push through, but in general, life sucks when you surround yourself or enforce artificial hard cut-offs.

I notice that you've just framed most knowledge creation/discovery as a form of gradient descent.

Which it is, of course.