Identifying Cardinal Number Usage: The Number 6 Example

Understanding the difference between cardinal and ordinal numbers is key to interpreting mathematical statements correctly. Cardinal numbers are used to express quantity, essentially answering the question "how many?". For instance, saying there are 5 apples uses '5' in a cardinal sense.

Ordinal numbers, on the other hand, are used to indicate position or order within a sequence. They answer the question "which one?". Examples include 'first', 'second', 'third', or '6th'.

Detailed Analysis of Number 6 in Statements

Let's examine each statement to see how the number 6 is used:

• Statement 1: 6 is the predecessor of 7

  This statement describes a relationship based on order. The term 'predecessor' refers to the number that comes immediately before another number in a sequence. This is an ordinal concept, not cardinal.

• Statement 2: She was sitting in the 6th row of the auditorium

  Here, '6th' indicates the specific position of the row. It answers "which row?" she was sitting in. This is a clear use of an ordinal number.

• Statement 3: There are 6 elements in a set

  This statement uses the number 6 to specify the total count or quantity of items within the set. It directly answers the question "how many elements are in the set?". This is the definition of using a number in a cardinal sense.

  In set theory, the number of elements in a set is called its cardinality.

• Statement 4: 6 is the successor of 5

  Similar to the predecessor, the term 'successor' refers to the number that comes immediately after another number in a sequence. This relates to order and is an ordinal concept.

Based on this analysis, the statement where the number 6 is used to represent quantity (how many) is the one using the cardinal sense.