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
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