1. ## The Number System

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

2. 1. The Natural numbers are the numbers used for counting. Number theorists choose 1 as the first natural number, while others (i.e. set theorists) choose to start with 0.

2 & 3. A set is a collection of objects or numbers. The members of a set are called elements. Set A is a subset of set B if all the elements of set A are in B. In this case, N is a subset of W because all the elements in N are elements of W.

3. ## not all elements...

Originally Posted by Chop Suey
1. The Natural numbers are the numbers used for counting. Number theorists choose 1 as the first natural number, while others (i.e. set theorists) choose to start with 0.

2 & 3. A set is a collection of objects or numbers. The members of a set are called elements. Set A is a subset of set B if all the elements of set A are in B. In this case, N is a subset of W because all the elements in N are elements of W.
What about 0? Not all elements of set N are found in W and vice-versa.

4. Originally Posted by magentarita
Not all elements of set N are found in W and vice-versa.

All elements of the Natural numbers set are found in the Whole numbers set.

However, the converse is not true. There is one element of the Whole Numbers set that is not included in the Natural numbers set. Namely, 0.

Originally Posted by magentarita

Read here: Natural number - Wikipedia, the free encyclopedia

for a better understanding of where zero fits in (or doesn't fit in) to these sets.

5. ## good

Originally Posted by masters

All elements of the Natural numbers set are found in the Whole numbers set.

However, the converse is not true. There is one element of the Whole Numbers set that is not included in the Natural numbers set. Namely, 0.

Read here: Natural number - Wikipedia, the free encyclopedia

for a better understanding of where zero fits in (or doesn't fit in) to these sets.
Thank for clearing that up for me.

6. Originally Posted by Wikipedia > Natural numbers
In mathematics, a natural number (also called counting number) can mean either an element of the set {1, 2, 3, ...} (the positive integers) or an element of the set {0, 1, 2, 3, ...} (the non-negative integers).
Originally Posted by Wikipedia > Whole numbers
The term whole number is used by various authors to mean either:

* the nonnegative integers (0, 1, 2, 3, ...)
* the positive integers (1, 2, 3, ...)
* all integers (..., -3, -2, -1, 0, 1, 2, 3, ...)
So there are about 6 possible combinations of defining N and W...