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section 2.4: complex numbers
... The real number line (below) exhibits a linear ordering of the real numbers. In other words, if c and d are real numbers, then exactly one of the following must be true: c < d , c > d , or c = d . ...
... The real number line (below) exhibits a linear ordering of the real numbers. In other words, if c and d are real numbers, then exactly one of the following must be true: c < d , c > d , or c = d . ...
Targil 5. Combinatorics again, but now with infinite sets. 1. Show that
... Yes. There are infinitely many Pythagorean triples a2 + b2 = c2, such as a = m2 – n2 , b = 2mn , c = m2 + n2. So the distance between points B(0,1) and Ak = ((k2 – 1)/2k, 0) is rational, for any k between 1 and 1000000. If we multiply all things by common denominator, or 1000000!, all coordinates an ...
... Yes. There are infinitely many Pythagorean triples a2 + b2 = c2, such as a = m2 – n2 , b = 2mn , c = m2 + n2. So the distance between points B(0,1) and Ak = ((k2 – 1)/2k, 0) is rational, for any k between 1 and 1000000. If we multiply all things by common denominator, or 1000000!, all coordinates an ...
