Billy is trying to convince Cynthia that all whole numbers are also natural numbers. To support his argument, Billy points out that 1, 2, 3, 4, 5, and 6 are all whole numbers and are also natural numbers. He goes on to argue that, by continuing the pattern, every integer greater than 6 will also be both a whole number and a natural number, thus making all whole numbers natural numbers.

Where has Billy made his error?

Question

Billy is trying to convince Cynthia that all whole numbers are also natural numbers. To support his argument, Billy points out that 1, 2, 3, 4, 5, and 6 are all whole numbers and are also natural numbers. He goes on to argue that, by continuing the pattern, every integer greater than 6 will also be both a whole number and a natural number, thus making all whole numbers natural numbers.  

Where has Billy made his error?

perl · Answer

whole numbers are the natural numbers plus zero . billy forgot to include zero 
whole #'s = { 0 , 1,2 ,3 , 4, 5, 6, ... } 

So whole numbers are an extension of natural numbers (by including zero).
In fact we can make further extensions to the natural numbers and whole numbers.
The 'integers' are the natural numbers, 0, and negatives of the natural numbers numbers. 
The 'rationals are a further extension by including numbers that are ratios like 1/5, 1/3, etc.