Find the Cardinality (0,5)

Problem

|(0,5)|

Solution

1. Identify the type of set provided. The notation (0,5) represents an open interval of real numbers between 0 and 5

2. Determine the nature of the elements. Since the interval consists of all real numbers x such that 0<x<5 it contains an uncountably infinite number of points.

3. Apply the property of interval cardinality. Any non-degenerate interval of real numbers (where the start point is less than the end point) has the same cardinality as the set of all real numbers ℝ

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

Final Answer

|(0,5)|=c

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