The Sum and Product of Finite Sequences of Real Numbers

Czeslaw Bylinski

Warsaw University, Bialystok

Supported by RPBP.III-24.C1.

Summary.

Some operations on the set of $n$-tuples of real numbers are introduced. Addition, difference of such $n$-tuples, complement of a $n$-tuple and multiplication of these by real numbers are defined. In these definitions more general properties of binary operations applied to finite sequences from [9] are used. Then the fact that certain properties are satisfied by those operations is demonstrated directly from [9]. Moreover some properties can be recognized as being those of real vector space. Multiplication of $n$-tuples of real numbers and square power of $n$-tuple of real numbers using for notation of some properties of finite sums and products of real numbers are defined, followed by definitions of the finite sum and product of $n$-tuples of real numbers using notions and properties introduced in [11]. A number of propositions and theorems on sum and product of finite sequences of real numbers are proved. As additional properties there are proved some properties of real numbers and set representations of binary operations on real numbers.

MML Identifier: RVSUM_1

Contents (PDF format)

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