| American Association for the Advancement of Science - American periodicals - 1892 - 614 pages
...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 - Science - 1892 - 604 pages
...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 pages
...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 - Algebra - 1896 - 242 pages
...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 - Philosophy, Modern - 1912 - 848 pages
...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 - Algebra - 1914 - 654 pages
...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 - Albegra - 1914 - 760 pages
...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 - Albegra - 1919 - 654 pages
...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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