Prove that the union of two disjoint denumerable sets is denumerable

[kealth]

Would someone please help me on the topic of Denumerability.

Prove that if A and B are disjoint denumerable sets then A union B is denumerable.

 

[Pere Callahan]

Welcome to PF!

How would you state the definition of denumerability?

 

[mathman]

Would someone please help me on the topic of Denumerability.

Prove that if A and B are disjoint denumerable sets then A union B is denumerable.

A and B being denumerable means there is are complete lists of the form:

a1, a2, a3,... for A
b1, b2, b3,... for B

The union can be listed as:

a1, b1, a2, b2, a3, b3, ...