Definitions of Rational, Irrational, and Mathematics

Date: 9 May 1995 12:08:14 -0400
From: J. C. Adamson
Subject: Irrational

Dear Doc:
        A student asked me why rational and irrational numbers are called 
by those names.  Always seemed intuitively OK to me, but in trying to get 
an answer for him,  I came up empty.  Couldn't find when and where the 
terms were first used, nor a derivation for them, in any of my references. 
Any ideas?
        2nd question:  I like to use definitions, and I give my students 
in basic college math a definition of "mathematics."  I use several 
definitions, but none seem really satisfactory.  How do you define the word?
        Thanks for your help.
                        J. C. Adamson
                        Colorado Institure of Art
                        Denver, CO

Date: 9 May 1995 17:20:42 -0400
From: Dr. Ken
Subject: Re: Irrational

Hello there!

I like the questions you've asked.  The term "rational" comes from the 
word "ratio," because the rational numbers are the ones that can be written 
in the ratio form p/q where p and q are integers.  Irrational, then, just 
means all the numbers that aren't rational.  

The term "mathematics" is one that seems to defy good definition.  It's 
kind of just whatever mathematicians are studying.  My dictionary defines 
math as "the study of numbers, their form, arrangement, and associated
relationships, using rigorously defined literal, numerical, and operational
symbols."  I don't like that definition very much, because there's lots and
lots of mathematics that's not about numbers.  My favorite definition is
that mathematics is "the study of patterns."  I like that.  

Etymologically speaking, mathematics comes from the Greek word, "mathema,"
which means "science," and that comes from the Greek word, "manthanein," 
which means "to learn."

-K