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Ordering Real Numbers

Date: 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   
Associated Topics:
High School Number Theory

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