- #1

The Captain

- 21

- 0

## Homework Statement

Define f: Z+ X Z+ -> Z+ by

f(a,b) = 2^(a-1)(2b-1) for all a,b in Z+

where Z+ is the set of all positive integers,

and X is the Cartesian product

## Homework Equations

## The Attempt at a Solution

If we assume (a,b) as ordered pairs and write them as follows:

(1,1) (1,2) (1,3) (1,4)...(a,b+n)

(2,1) (2,2) (2,3) (2,4)...(a+1,b+n)

.

.

.

.

.

.

.

(a+n,b)........(a+n,b+n)

Using diagonal processing, we deduce that f is one-one.

Now can we also assume it is onto because f(a,b) maps to exactly one ordered pair?

Last edited: