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 ),
Read more about this topic: Free Abelian Group
Famous quotes containing the words formal and/or sum:
“True variety is in that plenitude of real and unexpected elements, in the branch charged with blue flowers thrusting itself, against all expectations, from the springtime hedge which seems already too full, while the purely formal imitation of variety ... is but void and uniformity, that is, that which is most opposed to variety....”
—Marcel Proust (1871–1922)
“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)