Complex Linear Space of Complex Sequences
نویسنده
چکیده
The non empty set the set of complex sequences is defined by: (Def. 1) For every set x holds x ∈ the set of complex sequences iff x is a complex sequence. Let z be a set. Let us assume that z ∈ the set of complex sequences. The functor idseq(z) yields a complex sequence and is defined by: (Def. 2) idseq(z) = z. Let z be a set. Let us assume that z ∈ C. The functor idC(z) yielding a Complex is defined by: (Def. 3) idC(z) = z. One can prove the following propositions: (1) There exists a binary operation A1 on the set of complex sequences such that (i) for all elements a, b of the set of complex sequences holds A1(a, b) = idseq(a) + idseq(b), and (ii) A1 is commutative and associative.
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