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Edited by DarkSpyda04:
1/14/2014 5:39:32 AM
10
I'm confused: Algebraic Numbers
I'm reading this off a site
http://www.mathsisfun.com/numbers/algebraic-numbers.html
[quote]An algebraic number is any number that is a root of a non-zero polynomial with [b]rational coefficients. [/b]
Example: is √2 (the square root of 2) algebraic or transcendental?
√2 is the solution to x2 - 2 = 0, so is therefore algebraic
[/quote]
What? But √2 is [b]irrational![/b]
EDIT:
I get what a rational number is. I get what an irrational number is. But I don't get what an algebraic number is.
[quote]The root of an algebraic equation with rational coefficients.[/quote]
But I don't know what that's supposed to even mean!
-
[quote]The root of an algebraic equation with rational coefficients.[/quote] Let's define: coefficients are numbers that you multiply by a variable; in ax^2+bx+c, the coefficients are a, b, and c. Rational numbers are numbers that can be written as a fraction, or ratio; a/b, where a and b are integers and b isn't zero. For example, 5/3 which is 1.6 repeating forever, or 2/5, which is .4 that terminates, or even 8/1 which is 8. Algebraic equation means a polynomial, which is a function with more than one monomial, which are terms ax^2, or 54x. An example is x^3+ 3x^2+ 3x+ 1 A root is a number that you can plug into a function and you get zero. On a graph, it is the point on the x-axis that the line intersects, at which the y-value is zero. Put it all together and you define an algebraic number as a number that has some graph and some function, with rational numbers for coefficients, and that equals zero if you plug it in for x. I hope I helped.
