The Cantor pairing function is a pairing function
defined by
When we apply the pairing function to and we often denote the resulting number as
This definition can be inductively generalized to the Cantor tuple function
as
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“Through man, and woman, and sea, and star,
Saw the dance of nature forward far;
Through worlds, and races, and terms, and times,
Saw musical order, and pairing rhymes.”
—Ralph Waldo Emerson (18031882)
“Philosophical questions are not by their nature insoluble. They are, indeed, radically different from scientific questions, because they concern the implications and other interrelations of ideas, not the order of physical events; their answers are interpretations instead of factual reports, and their function is to increase not our knowledge of nature, but our understanding of what we know.”
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