One way to construct ∗ R is as a quotient of the ring of sequences, RN, by a suitable maximal ideal MAX, so that ∗ R = RN / MAX. Thus both the "square root of infinity" and "square of infinity" make sense when infinity is interpreted as a hyperreal number. An example of an infinite number in ∗ R is represented by the sequence 1, 2, 3, …. More @Wikipedia
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