That has little bearing to *teaching* math. In teaching, perfection is little more than rote memorization. In teaching, you have to explore your errors and unde

That has little bearing to *teaching* math. In teaching, perfection is little more than rote memorization. In teaching, you have to explore your errors and understand why they are happening. And in research math, some of the greatest insights come from encountering the errors in your own proofs. Yes, the final result is "perfect". Expecting the process (and especially the learning of the process) to be perfect is idiotic.