Ordering Real NumbersDate: 12/11/2000 at 02:09:36 From: Ray Subject: Ordering real numbers Can you describe how to order real numbers? Date: 12/11/2000 at 12:30:49 From: Doctor Rob Subject: Re: Ordering real numbers Thanks for writing to Ask Dr. Math, Ray. One way to tell which of a pair of real numbers is larger is by using their decimal expansions, and looking at the first decimal place in which they differ. Another way is to look at their difference. If it is zero, the numbers are equal. If it is not zero, see if it can be written as a square. If so, the minuend is larger than the subtrahend, and if not, the reverse is true. Another way is to approximate the real numbers by rational numbers. You can tell which of two rational numbers is the larger by using cross-multiplication. Real numbers close to the larger rational are larger than real numbers close to the smaller rational, provided "close" means a distance less than half the distance between the rational numbers. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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