Project #26576 - modulo and countability

three problems.

-construct a bijection between (0-1) and R. show it is a bijection.

-Zn (n!=0) passes the Zero Product Principle if ab=0(mod n) implies that either a=0(mod n) or b=0(mod n). Prove Zn pases the Zero Product Principle if and only if n is prime.  (= means conrguency)

-a number N is an alebraic integer if there exists a polynomial p(x) whose leading coefficient is 1 and p(N) = 0. Furthermore a irrational number N is quadratic if there exists a quadratic polynomial p(x) with p(N)=0. Let B be the set of all quadratic algebraic integers. Show that B is countable.

 Subject Mathematics Due By (Pacific Time) 04/02/2014 04:32 pm
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