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Btw, here's the link to the math paper guy's credentials.
http://www.math.sfu.ca/~jrg/
This is a very important question by the op...I hope everyone is seeking truth with a truly open mind not just getting caught up in winning an argument.
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As long as you have honest tactics, doing everything you can to win an argument is a pretty decent approach to education and learning. I've learned many challenging and important things because I spent hours and hours trying to refute them and realized I could not. The "honest tactics" caveat is very important, however, and I try my best.