Readings for Session 1 – Motivation for Sets and Whole Numbers

 

How are the numerals in the statement that follows used differently? Do they represent different types of numbers?

 

A class of MDEV 102 has 19 students and is held on the 2nd floor of Bridges in room number 269.

 

The sentence has four numerals representing numbers used in three different ways.

• The 102 and 269 are numerals called identification or nominal numbers since they are used to identify, name, or label.

• The 19 is a numeral for a cardinal number since it answers the question: How many elements are in a set?

• The 2 is a numeral for an ordinal number since it specifies a position in an ordering of a group of objects.

 

Definitions.  A number is the idea or abstract notion of quantity.

                     A numeral is the symbol(s) used to represent a number.

 

Example.  In the above example, the numeral 19 represents the number (quantity) of students in the class. The numeral 102 represents the number (identity) of the course. The numeral 2 represents the number (position) of the floor. The numeral 269 represents the number (location) of the room.

 

Analogy.  The difference in meaning between a number and a numeral is like the difference between you and your name. Your name represents you, but it is not who you are as a person. Similarly, a numeral represents a number, but it is not the value.

        

        The purpose of this session is to motivate the basic concepts that will be used throughout this chapter and the course. Our concern in this chapter is with whole numbers used as cardinal numbers in solving problems. In the next section, we will begin the formal development of the terminology we will use. But first, we illustrate how the concepts have humble beginnings with early humans and with small children.

 

 

  

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