The Number System of Algebra Treated Theoretically And Historically
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In any regular sequence a 1; a 2 , ••• a term o^ may always be found which itself, as well as each term which follows it, is either (1) numerically less than any assignable number, or (2) greater, than some definite positive rational number, or (3) less than some definite negative rational number.
In the first case the number a, which the sequence de- fines, is said to be zero, in the second positive, in the third negative.
29. The Four Fundamental Operations. Of the numbers defined by the two ...sequences : a l> a 2j a 3> ■■" a fi+l) "■ a n + v> '"> Pl> Pffl P3> •" P« PV + Ii •■• PlL + V} ••• (1) The sum is the number defined by the sequence : o-i + h a 2 + P» ••• ••• "n + i — pV + 1) • • • "-H- + " ~~ pV + v> . • • ■ (3) The product is the number defined by the sequence : a ip\> "spa ••• ••• (4) The quotient is the number defined by the sequence : a^ a 2 a a a, x + 1 tta+c A' A' pV pV + l' /W' For these definitions are consistent with the correspond- ing definitions for rational numbers ; they reduce to these elementary definitions, in fact, whenever the sequences 30 NUMBER-SYSTEM OF ALGEBRA.
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You can find similar books in the "Read Also" column, or choose other free books by Henry B Henry Burchard Fine to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In any regular sequence a 1; a 2 , ••• a term o^ may always be found which itself, as well as each term which follows it, is either (1) numerically less than any assignable number, or (2) greater, than some definite positive rational number, or (3) less than some definite negative rational number.
In the first case the number a, which the sequence de- fines, is said to be zero, in the second positive, in the third negative.
29. The Four Fundamental Operations. Of the numbers defined by the two ...sequences : a l> a 2j a 3> ■■"
What to read after The Number System of Algebra Treated Theoretically And Historically?
You can find similar books in the "Read Also" column, or choose other free books by Henry B Henry Burchard Fine to read onlineMoreLess
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