[Kenji]

>That's not really relevant. You only need to check if the equations hold if you don't understand the math involved. You've already lost at that point.

You have no idea how much understanding I gained by doing such 'quick checks', sometimes even during exams. Just a little sanity check to be sure you're still on track.

Besides, inserting 1 for both x and y is an actual mathematical proof that the equation does not hold! It's always a fantastic thing to strengthen your understanding with formal proofs that you came up with by yourself.

[fghvbnvbnfe]

I've always done those quick checks myself because otherwise I'm prone to making errors. They give me a quick answer of "no, you can't do this" but I never found they actually improved my understanding of anything. It just told me I can't do the thing I wanted to do and it was time to move to the next idea. It's a valid proof, but not one that really ever helped me get a grasp on what's happening.

Mostly it just means I'm in trouble and need to be really careful and do more checks because I'm working with things I don't understand fully.

For example, I've never needed to do that sort of check with adding fractions. I have enough understanding of what those numbers represent and how they work together that I've just never thought I might want to add numerators and denominators separately.