Readings for Session 7 – (Continued)  

More on Inequality Symbols

        The symbol  <  means “is strictly less than” since we are comparing the cardinal numbers for two sets where one set is equivalent to a proper subset of the other set.

 

Example:  If A ⊂ B, then n(A) < n(B).

 

Example:  If Abby has $4 and Billy has $5, then Abby has less money than Billy.

Symbolically:  If  n(A) = 4 and n(B) = 5, then  4 < 5.

The 4 is strictly less than the 5 and set A is equivalent to a proper subset of set B.

 

        The symbol  >  means “is strictly greater than” since we are comparing the cardinal numbers for two sets where one set is equivalent to a proper subset of the other set.

 

Example:  If A ⊂ B and B is a finite set, then n(B) > n(A).

 

Example:  If Ann has five apples and Bob has four bananas, then Ann has more apples than Bob has bananas.

Symbolically:  If n(A) = 5 and n(B) = 4, then  5 > 4.

The 5 is strictly greater than 4 and the set B is equivalent to a proper subset of set A.

 

        The symbol  ≤  means “is less than or equal to” since we are comparing the cardinal numbers for two sets where one set is equivalent to a subset of the other set. Remember that if a set is a subset of another set, the two sets may be the same set.

 

Example:  If A ⊆ B, then n(A) ≤ n(B).

 

Example:  The most goals the hockey team scored in a game this year was seven. This means that the number of goals scored in each game was less than or equal to seven.

Symbolically:  If n(G) = g where G is the set of individual goals scored in a game this year, then g ≤ 7.

The set G is equivalent to a subset of set L where L is the goals scored in a game with seven goals. Note that either g < 7 or g = 7.

 

Example:  If n(A) = 6 and n(B) = 6, then  6 ≤ 6.

In this case, the two sets are equivalent. Note that in this case, we also have 6 = 6.

 

        The symbol  ≥  means “is greater than or equal to” since we are comparing the cardinal numbers for two sets where one set is equivalent to a subset of the other set.

 

Example:  If A ⊆ B, then n(B) ≥ n(A).

Example:  We hope to make a profit of at least $35 when we sell the table. This means that the amount of profit should be greater than or equal to $35.

Symbolically:  If P is the set of dollars of profit, then n(P) ≥ 35.

A set containing 35 dollars is equivalent to a subset of set P.
Note that either n(P) > 35 or n(P) = 35.

  

      

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