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### Transcendental numbers

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Date: 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?

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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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Associated Topics:
High School Transcendental Numbers

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