@MISC{RVSUM_1.MIZ,
  AUTHOR = {Byli\'nski, Czes{\l}aw},
  TITLE = {The Sum and Product of Finite Sequences of Real Numbers},
  DAY = {11},
  MONTH = {May},
  YEAR = {1990},
  ADDRESS1 = {Warsaw University\\Bia{\l}ystok},
  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 \cite{FINSEQOP.ABS} are used.
Then the fact that certain 
properties are satisfied by those operations is demonstrated directly
from \cite{FINSEQOP.ABS}.
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 \cite{SETWOP_2.ABS}.
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.}}

