For countable set G, H = {f : N → G : f is injective} where...

For countable set G, H = {f : N → G : f is injective} where N is the natural numbers. What is the cardinality of H. Prove it.

Expert Solution

Colby Messinger answered 2 years ago

Prove a (Dedekind) set is inﬁnite iff there exists an injective function f : N→ A....

Prove a (Dedekind) set is inﬁnite iff there exists an injective function f : N→ A. please help prove this clearly and i will rate the best answer thank you

1)Show that a subset of a countable set is also countable. 2) Let P(n) be the...

1)Show that a subset of a countable set is also countable. 2) Let P(n) be the statement that 13 + 23 +· · ·+n3 =(n(n + 1)/2)2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis....

1. Prove or disprove: if f : R → R is injective and g : R...

1. Prove or disprove: if f : R → R is injective and g : R → R is surjective then f ◦ g : R → R is bijective. 2. Suppose n and k are two positive integers. Pick a uniformly random lattice path from (0, 0) to (n, k). What is the probability that the first step is ‘up’?

If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________

If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________ Given the function: y=sin(4x)+e^-3x and dx/dt = 3 when x=0. Then dy/dt = ________________ when x=0. Let f(x) = ln (√x). The value of c in the interval (1,e) for which f(x) satisfies the Mean Value Theorem (i.e f'(c)= f(e)-f(1) / e-1 ) is: _________________________ Suppose f(x) is a piecewise function: f(x) = 3x^2 -11x-4, if x ≤ 4 and f(x) =...

Prove or disprove each of the followings. If f(n) = ω(g(n)), then log2(f(n)) = ω(log2g(n)), where...

Prove or disprove each of the followings. If f(n) = ω(g(n)), then log2(f(n)) = ω(log2g(n)), where f(n) and g(n) are positive functions. ω(n) + ω(n2) = theta(n). f(n)g(n) = ω(f(n)), where f(n) and g(n) are positive functions. If f(n) = theta(g(n)), then f(n) = theta(20 g(n)), where f(n) and g(n) are positive functions. If there are only finite number of points for which f(n) > g(n), then f(n) = O(g(n)), where f(n) and g(n) are positive functions.

Given, op: (λ(n) (λ(f) (λ(x) (((n (λ(g) (λ(h) (h (g f))))) (λ(u) x)) (λ(u) u))))) zero:...

Given, op: (λ(n) (λ(f) (λ(x) (((n (λ(g) (λ(h) (h (g f))))) (λ(u) x)) (λ(u) u))))) zero: (λ(f) (λ(x) x)) one: (λ(f) (λ(x) (f x))) two: (λ(f) (λ(x) (f (f x)))) three: (λ(f) (λ(x) (f (f (f x))))) i. (4 pt) What is the result of (op one)? ii. (4 pt) What is the result of (op two)? iii. (4 pt)What is the result of (op three)? iv. (3 pt) What computation does op perform?

If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))

Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE. Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS...

Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE. Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS TRUE

Prove and give a counterexample: If N ⊲ G and G ⊲ H, then N ⊲...

Prove and give a counterexample: If N ⊲ G and G ⊲ H, then N ⊲ H. Please write an explanation with some details

Consider the relation R= {A, B, C, D, E, F, G, H} and the set of...

Consider the relation R= {A, B, C, D, E, F, G, H} and the set of functional dependencies: FD= {{B}—> {A}, {G}—> {D, H}, {C, H}—> {E}, {B, D}—> {F}, {D}—>{C}, {C}—> {G}} 1) Draw FD using the diagrammatic notation. 2) What are all candidate keys for R? 3) If delete {C}—>{G} and change {C, H}—> {E} to {C, H}—> {E, G}, what are all candidate keys for R

Question