Question

In: Advanced Math

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

Solutions

Expert Solution


Related Solutions

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.
Let F be a finite field. Prove that there exists an integer n≥1, such that n.1_F...
Let F be a finite field. Prove that there exists an integer n≥1, such that n.1_F = 0_F . Show further that the smallest positive integer with this property is a prime number.
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’?
Some hints: use the definition: f is a function iff a = b implies f(a) =...
Some hints: use the definition: f is a function iff a = b implies f(a) = f(b) and recall that in informal proofs we show an implication by assuming the if part of the implication, and then deducing the then part of the implication. The base case will show that a = b implies f(a) = f(b) when f(x) = c0 (a constant function). The inductive case will assume a = b implies f(a) = f(b) for degree k, and...
Let {an}n∈N be a sequence with lim n→+∞ an = 0. Prove that there exists a...
Let {an}n∈N be a sequence with lim n→+∞ an = 0. Prove that there exists a subsequence {ank }k∈N so that X∞ k=1 |ank | ≤ 8
Classify each function as injective, surjective, bijective, or none of these. a) f1 : N -->...
Classify each function as injective, surjective, bijective, or none of these. a) f1 : N --> Q defined by f1 (n) = n/(n+1) b) f2: Z --> Z defined by f2(n) = n2 c) f3 : N --> N defined by f3(n) = n3 d) f4 : B --> (0, infinity) defined by f4 (C) = the area of C, where B is the set of all circles in the firs quadrant that are simultaneously tangent to both the positive...
If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))
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
For f: N x N -> N defined by f(m,n) = 2m-1(2n-1) a) Prove: f is...
For f: N x N -> N defined by f(m,n) = 2m-1(2n-1) a) Prove: f is 1-to-1 b) Prove: f is onto c) Prove {1, 2} x N is countable
Prove that there exists integers m and n such that 15m + 12n = 3 Please...
Prove that there exists integers m and n such that 15m + 12n = 3 Please do not prove by assuming m=1 and n=-1, I'd like to prove by not assuming any actual numbers.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT