SOLUTION: Why is the set of odd numbers equivalent to the set of whole numbers?

Question 395724: Why is the set of odd numbers equivalent to the set of whole numbers?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
It's because there exists a bijective function that maps the odd numbers to the set of whole numbers.

If A = {...-5, -3, -1, 1, 3, 5...} and B = {0, 1, 2, 3, ...} then if we let for all x contained in A, we get the set {1, 1, 3, 3, 5, 5, ...} (after reordering). Subtracting one from every other term starting with the first term we get {0, 1, 2, 3, ...}, or B. Therefore the two sets have the same cardinality, or .
RELATED QUESTIONS
Why are the infinite sets: set of natural numbers, set of integers, set of odd numbers... (answered by tommyt3rd)

For what operation is the set of integers not closed? Odd integers Natural numbers... (answered by stanbon)

V is the set of all odd numbers W =... (answered by Edwin McCravy)

Consider the set of whole numbers from 1 to 10, inclusive. List the numbers that meet... (answered by fractalier)

The number -4 does not belong to which set of numbers? rational numbers integers real... (answered by EdenWolf)

Is the following true or false? The set of whole numbers is closed under subtraction... (answered by askmemath)

Determine whether the statement is true or false. If the statement is false, give a... (answered by solver91311)

Is the following set of numbers a perfect triple? Why or why not? 8, 10,... (answered by solver91311)

True or False??? The set of intergers is the same as the set of additive inverses of... (answered by longjonsilver)