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PlanetMath: normal number (551 words) |
 | Borel also proved that almost all real numbers are absolutely normal, in the sense that the numbers that are not absolutely normal form a set of Lebesgue measure zero. |
| The first absolutely normal number was constructed by Sierpinski in 1916, and a related construction led to a computable absolutely normal number in 2002. |
| Proving the normality of an irrational number is daunting already, proving that it is absolutely normal may even be out of reach. |
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Algebraic Forms - LoveToKnow 1911 (16161 words) |
| Arithmetical groups, connected with the theory of quadratic forms and other branches of the theory of numbers, which are termed "discontinuous," and infinite groups connected with differential forms and equations, came into existence, and also particular linear and higher transformations connected with analysis and geometry. |
| In the theory of forms we seek functions of the coefficients and variables of the original quantic which, save as to a power of the modulus of transformation, are equal to the like functions of the coefficients and variables of the transformed quantic. |
| The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form. |
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