Transcendental numbersDate: Thu, 17 Nov 1994 16:22:42 -0800 (PST) From: "Judy M. Young" Subject: transcendental numbers We just learned about e today and how it is similar to pi because it is irrational without a radical. Are there any other transcendental numbers, and if so, how are they used? Leslie Young 11th grade Date: Fri, 18 Nov 1994 20:26:40 -0500 (EST) From: Dr. Ken Subject: Re: transcendental numbers Hello there Judy! As a matter of fact, there are a whole SLEW of transcendental numbers. In fact, MOST numbers are transcendental. Here's how it works. See, a number is called "algebraic" if it's the root of a polynomial with integer coefficents. The definition of a transcendental number is one that's not algebraic. You can show that the number of algebraic numbers is pretty small compared to the number of real numbers (the way you say this in Math-ese is that the set of algebraic numbers has "measure zero"). So the numbers left over (the transcendental numbers) are pretty numerous (ha!). You certainly couldn't count them. Pi and e are certainly the most famous transcendental numbers, and they're the only ones I ever hear about that have been given names. I wonder if any of the other Math Doctors know of any others (are you guys listening?)! I hope this helps! -Ken "Dr." Math |
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