I am reviewing my notes for a class review quiz. The quiz will test our knowledge of the number system.

I will share what was given in class some time ago.

Our teacher denoted the set of natural numbers by an upper case letter N.

He said:

N = {1, 2, 3, 4...+infinity}

Our teacher stated that the set natural numbers does not include the number zero but never explained why that is the case.

He went on to write that the set of whole numbers will be denoted in our class by the upper case letter W.

He said:

W = {0, 1, 2, 3, 4...+ infinity}

He went on to say that"N is a subset of W"but never explained why that is the case.

QUESTIONS:

(1) Why is zero not included in the set of natural numbers?

(2) Why is N a subset of W in the above case?

(3) What exactly is a subset anyway?

Thanks