[arsenide]

First year pure math: that statement in reference to these introductory courses.

I don't agree that using this is a "serious handicap" to my capacity for thinking syntactically. It is just another tool to be used when applicable to generate understanding: use an example and see how it follows the rigorous definitions. I lose nothing by doing this when it is useful.

Even in this link, Dr. Tao agrees that it is not a good idea to look at statements on a strictly formal level. In a greater sense this is what I was getting at: play with some examples or with some of the assumptions and see what happens in order to get initial or further understanding. Did I misunderstand the stated point? What was said just prior but in reference to "this[1]" is not supported by Dr. Tao in his post.

Relevant quote: "'fuzzier' or 'intuitive' thinking (such as heuristic reasoning, judicious extrapolation from examples, or analogies with other contexts such as physics) gets deprecated as 'non-rigorous'. All too often, one ends up discarding one’s initial intuition and is only able to process mathematics at a formal level, thus getting stalled at the second stage of one’s mathematical education."