Numbers in General
The rational numbers are beautifully suited to arithmetic, being closed under +, −, x, ÷, but they are inadequate for geometry. Their inadequacy is exposed by the Pythagorean theorem, according to which the diagonal x of the unit square (Figure 3.1.1) satisfies x2 = 12 + 12 = 2. We can see that no rational number x satisfies this equation as follows.
KeywordsFundamental Theorem Algebraic Number Irrational Number Pythagorean Theorem Rational Length
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