Find the Cardinality (2,1)

Problem

|(2,1)|

Solution

1. Identify the type of mathematical object provided. The notation (2,1) represents an ordered pair, which is a single element in a set (specifically, an element of the Cartesian product ℝ×ℝ or ℤ×ℤ.

2. Define cardinality for this context. The cardinality of a set is the number of elements it contains. However, when applied to a single ordered pair treated as a set-theoretic object, we look at the number of elements within that specific tuple.

3. Count the number of components in the ordered pair. The pair contains two distinct components: the first coordinate 2 and the second coordinate 1

4. Determine the result. Since there are exactly two entries in the tuple, its cardinality (or length) is 2.

Final Answer

|(2,1)|=2

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