3. Given any nonempty set A equipp +: A x A → A, for any two nonen such that J is a permutation of I ( call fon (a) of al
3. Given any nonempty set A equipp +: A x A → A, for any two nonen such that J is a permutation of I ( call fon (a) of al
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Proposition 3.3. Given any nonempty set A equipped with an associative and commutative
binary operation+: A x AA, for any two nonempty finite sequences I and J of distinct
natural numbers such that J is a permutation of I (in other words, the underlying sets of I
and J are identical), for every sequence (ai)ies of elements in A, we have
Σαα-Σκαι
=
αEI
aEJ
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