Cardinal Assignment
In set theory, the concept of cardinality is significantly developable without recourse to actually defining cardinal numbers as objects in theory itself (this is in fact a viewpoint taken by Frege; Frege cardinals are basically equivalence classes on the entire universe of sets which are equinumerous). The concepts are developed by defining equinumerosity in terms of functions and the concepts of one-to-one and onto (injectivity and surjectivity); this gives us a pseudo-ordering relation
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Famous quotes containing the word cardinal:
“What people don’t realize is that intimacy has its conventions as well as ordinary social intercourse. There are three cardinal rules—don’t take somebody else’s boyfriend unless you’ve been specifically invited to do so, don’t take a drink without being asked, and keep a scrupulous accounting in financial matters.”
—W.H. (Wystan Hugh)