However, the act of creating mathematical proofs is also important in building a fundamental analytical mind. Proofs are a surprising area where mathematics serves a highly useful realistic purpose, also, but not in ways you might expect! For example, the section below on conditionals is vital to understanding the most basic of computer programming-so much so, in fact, that we can't even say that a machine is entirely programmable without it. All of those equations you've heard before-like the familiar Pythagorean theorem, a 2 + b 2 = c 2-have been proved at least once (and in that case many, many times over) in the history of mathematics. One of the weird things about the field of mathematics in general is that all mathematically true statements are either postulates or provable from postulates.
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