 | American Association for the Advancement of Science - 1892 - 614 lapas
...has been perfected by the full use of the complex unit a-\-bi, forming thus, in the words of Cayley, a "Universe complete in itself, such that starting in it we are never led out of it." We have in fact a double algebra as the instrument for the complete treatment of all higher analysis,... | |
 | American Association for the Advancement of Science - 1892 - 604 lapas
...has been perfected by the full use of the complex unit a-\-bi, forming thus, in the words of Cayley, a "Universe complete in itself, such that starting in it we are never led out of it." We have in fact a double algebra as the instrument for the complete treatment of all higher analysis,... | |
 | American Association for the Advancement of Science - 1892 - 606 lapas
...has been perfected by the full use of the complex unit a-\-bi, forming thus, in the words of Cayley, a "Universe complete in itself, such that starting in it we are never led out of it." We have in fact a double algebra as the instrument for the complete treatment of all higher analysis,... | |
 | Arthur Lefevre - 1896 - 242 lapas
...whether with sound philosophy or essential contradiction of terms I will not attempt to discuss, " There may very well be, and perhaps are, numbers in...with such numbers (if any), we must start with them." * 105. I believe that very few, even among students of mathematics, are aware of the chaos of their... | |
 | John Theodore Merz - 1912 - 848 lapas
...without the addition of the imaginary unit, but that with the introduction of a second unit "numbers form a universe complete in itself, such that, starting...perhaps are, numbers in a more general sense of the term ; but in order to have to do with such numbers (if any) we must start with them " (Cayley in art. "Equation,"... | |
 | Sir Thomas Percy Nunn - 1914 - 654 lapas
...word " number " in algebra always to mean "complex number," we can say with Cay ley that "numbers form a universe complete in itself, such that, starting in it, we are never led out of it ". These observations have an obvious geometrical intrepretation. Eeal numbers correspond to points... | |
 | Thomas Percy Nunn, Sir Thomas Percy Nunn - 1914 - 760 lapas
...of § 1) that complex numbers must be regarded as the typical numbers of algebra because they " form a universe complete in itself, such that, starting in it, we are never led out of it ". In Ex. XCVI we begin a series of investigations which illustrate this important statement. The statement... | |
 | Sir Thomas Percy Nunn, Thomas Percy Nunn - 1919 - 654 lapas
...of § 1) that complex numbers must be regarded as the typical numbers of algebra because they " form a universe complete in itself, such that, starting in it, we are never led out of it ". In^ Ex. XCVI we begin a series of investigations which .illustrate this important statement. The... | |
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We have in fact a double algebra as the instrument for the complete treatment of all higher analysis, except that in which one of higher multiplicity is used. The field of Quantics has been brilliantly cultivated by Cayley, Sylvester and others. 