- #1
David Carroll
- 181
- 13
Greetings in the name of Jah-gonaut, ladies and gents. I have a question. Is there a strictly algebraic way of coding the notion "whole number value of", specifically for an irrational number?
I know that one way of coding the notion "absolute value of" some number is taking the square root of the square. Can something similar be done to code for "whole part" of some number, using only algebraic symbols or numbers? Namely, in my case, can some kind of manipulation of symbols be done with the irrational part of a solution to some polynomial equation {by which I mean the "sqrt(b2 + 4ab)" part of the solution)}, using ONLY the symbols a or b?
For example, let's take the two solutions to the polynomial equation x2 + 21x - 155 = 0:
-26.7864974749... and 5.7864974749...
I want to separate the decimal expansion from the whole value 5 for the second solution. But I want to perform this step using only algebraic symbols, pretending - say - that I'm some machine that doesn't otherwise know the command "separate the whole part from the decimal expansion".
Can I perform some finite manipulation of the symbols a, b, or c (from the polynomial formula) to do this?
I know that one way of coding the notion "absolute value of" some number is taking the square root of the square. Can something similar be done to code for "whole part" of some number, using only algebraic symbols or numbers? Namely, in my case, can some kind of manipulation of symbols be done with the irrational part of a solution to some polynomial equation {by which I mean the "sqrt(b2 + 4ab)" part of the solution)}, using ONLY the symbols a or b?
For example, let's take the two solutions to the polynomial equation x2 + 21x - 155 = 0:
-26.7864974749... and 5.7864974749...
I want to separate the decimal expansion from the whole value 5 for the second solution. But I want to perform this step using only algebraic symbols, pretending - say - that I'm some machine that doesn't otherwise know the command "separate the whole part from the decimal expansion".
Can I perform some finite manipulation of the symbols a, b, or c (from the polynomial formula) to do this?