Tuesday

January 27, 2015

January 27, 2015

Posted by **Samantha** on Saturday, December 4, 2010 at 3:23pm.

- discrete math -
**MathMate**, Saturday, December 4, 2010 at 7:35pmSo the question is:

A={m∈ℤ : m=3k+7 ∃k∈ℤ^{+}}

Prove that A is countably infinite by defining a function f : ℤ -> A and proving that f is bijective.

A function f is bijective if and only if its inverse is also a function.

Since the inverse of f is relative easy to find, all you need is to prove that the inverse is a function.

If f is bijective (i.e. one-to-one and onto), and if the domain is countably infinite, the range of f, i.e. A, must be also.

**Answer this Question**

**Related Questions**

discrete math - Let f:ℤ+ → ℤ+ be the function defined by: for...

computer science - Write a method printBackwards that prints an array of ...

discrete math - 1)prove that if x is rational and x not equal to 0, then 1/x is ...

Discrete Math - Theorem: For every integer n, if x and y are positive integers ...

discrete math - If a and b are positive integers, prove that; ab = gcd(a,b)*lcm(...

math - Let f:ℤ+ → ℤ+ be the function defined by: for each x &#...

math help please - Let f:ℤ+ → ℤ+ be the function defined by: ...

Data Structures and Algorithms - Given integers R,M with M≠0, let S(R,M) ...

discrete math - which positive integers less than 12 are relatively prime to 13 ...

algebra - Find the sum of all positive integers c such that for some positive ...