Final answer:
In mathematics, the term 'cardinality' refers to the size or number of elements in a set. When comparing the set (0, 1) to the set of all real numbers between -1 and 1 denoted by r, both sets have an infinite number of elements, resulting in the same cardinality.
Step-by-step explanation:
In mathematics, the term 'cardinality' refers to the size or number of elements in a set. When we say that two sets have the same cardinality, it means that they have the same number of elements. In this case, we are comparing the set {(0, 1)} to the set of all real numbers between -1 and 1, denoted by the symbol r.
Both sets have an infinite number of elements, so they have the same cardinality. Despite (0, 1) having only two elements, the set of real numbers between -1 and 1 is uncountably infinite. This means that although (0, 1) seems smaller, it has the same cardinality as r.
Thus, (0, 1) and r have the same cardinality.