A formal sum of elements of a given set B is an element of the free abelian group with basis B. In other words, given a set B, let G be the unique (up to isomorphism) free abelian group with basis B. For elements and (where there must be an such that for all ),
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Famous quotes containing the words formal and/or sum:
“It is in the nature of allegory, as opposed to symbolism, to beg the question of absolute reality. The allegorist avails himself of a formal correspondence between “ideas” and “things,” both of which he assumes as given; he need not inquire whether either sphere is “real” or whether, in the final analysis, reality consists in their interaction.”
—Charles, Jr. Feidelson, U.S. educator, critic. Symbolism and American Literature, ch. 1, University of Chicago Press (1953)
“They are but beggars that can count their worth,
But my true love is grown to such excess
I cannot sum up sum of half my wealth.”
—William Shakespeare (1564–1616)