Readings for Session 7 – Order and Addition of Whole Numbers

 

How do sets relate to the comparison being made in the following problem?

Sam has three apples and Terry has five oranges. Who has more pieces of fruit? 

An apple.An apple.An apple.
 An orange.An orange.An orange.An orange.An orange.

        Terry has more fruit. We illustrate with the set concepts of 1-1 correspondence and subset. The three apples can only be set up with a 1-1 correspondence with three of the oranges. Two of the oranges cannot be paired with any apples in the 1-1 correspondence. That is, the apples can only be paired with a subset of the set of oranges. Since the set of apples is equivalent to a proper subset of the set of oranges, Sam has fewer apples than Terry has oranges.

        The relationship above motivates the definitions for ordering the natural and whole numbers that we give in this session. We begin with a quick reminder of the definitions of the sets of natural numbers and whole numbers.

 N = Natural numbers = {1, 2, 3, 4, 5, 6, . . . }.  Also, called  “counting numbers”.

 W = Whole numbers = {0, 1, 2, 3, 4,  . . . }.

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