By Voroshilov A. A., Kilbas A. A.
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Extra info for A Cauchy-Type Problem for the Diffusion-Wave Equation with Riemann-Liouville Partial Derivative
As a result the set of atoms never leaps to aleph-one and the disturbing contradiction does not arise. Cantor was convinced that his endless hierarchy of alephs, each obtained by raising 2 to the power of the preceding aleph, represented all the alephs there are. There are none in between. Nor is there an Ultimate Aleph, such as certain Hegelian philosophers of the time identified with the Absolute. The endless hierarchy of infinities itself, Cantor argued, is a better symbol of the Absolute. All his life Cantor tried to prove that there is no aleph between aleph-null and C, the power of the continuum, but he never found a proof.
Now move the unit line a distance of one unit in a direction perpendicular to the line (b) . This generates a unit square. Label one corner 0, then number the points from 0 to 1 along each of the two lines that meet at the zero corner. With these x and y coordinates we can now label every point on the square with a n ordered pair of numbers. I t is just as easy to visualize the next step. Shift the square a unit distance in a direction at right angles to both the x and the y axes ( c ) . The result is a unit cube.
The challenge is to position three pennies in such a way that the surfaces of two heads are wholly to the right of the line and the surfaces of two tails are wholly to the left of the line. ADDENDUM TRIANGULAR SOLITAIRE obviously can be played on triangular matrices with borders other than the triangle: hexagons, rhombuses, six-pointed stars, and so on. It also can be played with varying rules such as: (1) Jumps parallel to one side of the unit cell can be prohibited. See the 15-triangle solitaire problem in Maxey Brooke, Fun for the Money (Scribner's, 1963), page 12.