Prove that √2 is algebraic (For extreme beginners :D)
Also prove that √2+√3 is algebraic
-
UP 0 DOWN 0 0 8
8 Answers
62no it is the set of those numbers which are the roots of a polynomial with integer coefficients
example √-1 since it is the root of the equation x2+1 = 0
1then \sqrt{2} is algebraic as it is a root of x2-2=0
\sqrt{2}+\sqrt{3} is root of the eqn
x2-5-\sqrt{6}=0
or x4+10x2+19=0 so it is algebraic
62A trivia for you..
The number of algebraic numbers is countable. (Equal in number to the number of Natural numbers!)
Since each rational number is algebraic (Which should be obvious ;)), the number of rational numbers is also countable.
(May be you wont understand the proof.. if you are interested I will give you the links or try to explain myself)
1Nishant sir can you give an example of a non algebraic number please?
EDIT: also sir can you explain me how can the number of rational numbers be countable :(
62teh countability of rational numbers is proved by giving a one one onto mapping between the set of rationals and the set of Natural numbers..
The logic is very easy.. just think it once.. if you cant then i will post it tomorrow with a diagram :)
and yeah pi, e etc are all non algebraic