[math-fun] What is the correct word for . . .
. . . real numbers that can be expressed using integers, addition, subtraction, multiplication, division, and integer roots and powers -- starting with integers or rationals? How about all such (real or) complex numbers? (As distinguished from the rest of the algebraic numbers.) --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
I use "radical integers" for the integer subset of these. Maybe "radical rationals" & "real radical rationals"? Are you including the cube roots of complex numbers that can't be expressed in real radicals, like cbrt(2+i)? Or the RealParts of these, as (cbrt(2+i)+cbrt(2-i))/2? Rich ---- Quoting Dan Asimov <dasimov@earthlink.net>:
. . . real numbers that can be expressed using integers, addition, subtraction, multiplication, division, and integer roots and powers -- starting with integers or rationals?
How about all such (real or) complex numbers?
(As distinguished from the rest of the algebraic numbers.)
--Dan
________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
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These are, in other words, algebraic numbers with solvable Galois group, which may be a reasonable way to specify them. Do they deserve to have a 1-word name? It would be tempting to call them "radical numbers" except that they're not actually so radical, they're comparatively tame among algebraic numbers. "Constructible numbers" is already taken, by the special case of algebraic numbers whose Galois group is a 2-group. Bill On Feb 15, 2010, at 2:41 PM, Dan Asimov wrote:
. . . real numbers that can be expressed using integers, addition, subtraction, multiplication, division, and integer roots and powers -- starting with integers or rationals?
How about all such (real or) complex numbers?
(As distinguished from the rest of the algebraic numbers.)
--Dan
________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
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Perhaps these may suggest something suitable: Solvable numbers? Solvable algebraics? Expressible numbers? Expressionable numbers? Calculable numbers? ... At 01:08 PM 2/15/2010, Bill Thurston wrote:
These are, in other words, algebraic numbers with solvable Galois group, which may be a reasonable way to specify them. Do they deserve to have a 1-word name? It would be tempting to call them "radical numbers" except that they're not actually so radical, they're comparatively tame among algebraic numbers. "Constructible numbers" is already taken, by the special case of algebraic numbers whose Galois group is a 2-group. Bill On Feb 15, 2010, at 2:41 PM, Dan Asimov wrote:
. . . real numbers that can be expressed using integers, addition, subtraction, multiplication, division, and integer roots and powers -- starting with integers or rationals?
How about all such (real or) complex numbers?
(As distinguished from the rest of the algebraic numbers.)
--Dan
________________________________________________________________________________________
"Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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