Recent content by h.shin

Homework Statement Let a be a fixed positive rational number. Choose(and fix) a naural number M > a. a) For any n\inN with n\geqM, show that (a^n)/(n!)\leq((a/M)^(n-M))*(a^M)/(M!) b)Use the previous prblem to show that, given e > 0, there exists an N\inN such that for all n\geqN, (a^n)/(n!)...

Homework Statement Given M \in N, show that there exists an X \in N such that for all n \geq X , n^2+n+1 \succ M Homework Equations The Attempt at a Solution Since both M and X are natural numbers and I am just trying to prove the existence of a certain natural number X, I...

yes, well n--->2n is injective but not surjective

Homework Statement Show that for a set S, there exists an injective function \Phi : N \rightarrow S if and only if there exists an injective, but non-surjective function f : S \rightarrow S. (Sets S satisfying this condition are called innite sets.) Homework Equations The...

what does a graph of a function mean. Well, doesn't it just mean that it represents the relationship between the domain and the co domain? and what could go wrong..? Well, i feel like the only things that can go wrong are if there are two values of codomain for one value of domain. Or, there...

Homework Statement If A and B are sets, prove that a subset \Gamma\subset A X B is the graph of some function from A to B if and only if the first projection \rho: \Gamma\rightarrow A is a bijection. Homework Equations The Attempt at a Solution I first thought that i should...