Integration by me
本文即將參考 Walter Rudin 的 Principles of mathematical analysis 砍掉重練，敬請期待！
In the viewpoint of a student learning calculus for the first time, it would add a huge complexity if formal definitions are introduced, and students would be baffled and scared away from calculus.
Even if formal treatment is necessary, it’s still better to be introduced it in the second, advanced course of calculus.
The word “formal" as in formal definition is interesting, it might mean official or authenticated, but for me it much more means “formal". It is written in a strict form, so that we can play around logically-unequivocal.
Students are scared away from articles full of unexplained jargons. However, there is no intrinsic difficulty in jargons. People abort reading jargoned articles, as they give up newspapers in a foreign language.
I believe that if most terms are defined unambiguously via simpler terms, leaving the simplest terms undefined, a math article should be as readable as newspaper. Leaving simplest terms undefined is necessary because we want math to describe as many things (in everyday life) as possible. These terms are too easy to explain, such as dot, line and even not and if. If we are forced to explain these terms, it is inevitable that we must use more complex terms.
I would like to share a comic describing people’s prejudice on math.
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