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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!
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[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.
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Edited by DarkSpyda04: 1/17/2014 7:12:40 AMI think the definition of algebraic numbers is so hard to understand because the rules keep changing and there is no solid "this is how you can identify an algebraic number." First you tell me it has to be a root, then you tell me it doesn't necessarily have to be a root, then you tell me ALL rational numbers are algebraic (what happened to it has to be a root?), then you tell me irrational numbers can be algebraic. It's like trying to comprehend what Earth civilization will look like in Y3K. Just thinking about it makes my head spin.
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the number itself doesn't have to be rational you silly thing! all you've gotta worry about are the coefficients in the [i]equation![/i]
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10 RepliesEdited by Seggi: 1/14/2014 11:50:33 PMyo, pure maths major here. Do you know what a root of a polynomial is?
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Don't worry about it it never comes up in higher math
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I just don't get it, dude. I have no idea what "algebraic number" refers to. I can pick a number up out of a raffle and tell you it's an odd number, a prime, or rational but I can't tell you whether or not that number is algebraic.
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Porch math
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5 RepliesI try not to think about math because it doesn't make sense. I just do the work.
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To be honest math has been nothing but a pain ever since I started learning it. Every step of the way it's another brick wall and another thing that I can't comprehend. I don't want to learn math simply because I feel as though it's something I need to brush up on or because I need to take the SAT, but I think I keep putting myself between a rock and a hard place for the reason that I never finish anything that I start, and I want to for once keep my word that I can endure. Usually when the fire gets too hot I jump ship. Now I feel as though I'm burning alive. By now my brain is not even trying to understand algebraic numbers and I'm not sure I can. Even then I still have imaginary numbers, factoring, and other things that make my head explode.
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Yeah, but the coefficient of the polynomial that √2 is a root of is rational. An algebraic number doesn't have to be rational.
