Find the Cardinality (-3,7)

Problem

|(−3,7)|

Solution

1. Identify the type of set given. The notation (−3,7) represents an open interval on the real number line ℝ

2. Determine the nature of the elements within the interval. Since the interval contains all real numbers x such that −3<x<7 it is a non-degenerate interval of real numbers.

3. Apply the definition of cardinality for intervals of real numbers. Any interval (a,b) where a<b contains uncountably many points and has the same cardinality as the set of all real numbers ℝ

4. State the cardinality using the standard symbol. The cardinality of the continuum is denoted by c or 2

Final Answer

|(−3,7)|=c

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