By Régis petit, Michel Lambert

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**Sample text**

Amongst his various accomplishments, the visitor was an excellent chess player and before long he defeated the best of them in the King's court. Very pleased, the King asked the scholar what reward he wished to receive from the royal hands. After some thought, the scholar said: "Sir, give me grains of rice which will be adequate to fill up a chessboard in the following fashion. Number the squares on the board in any fashion, from 1 to 64. 1 Chessboard squares filled with rice in an increasing sequence.

Bib2b3 . . is also in С but В differs from each Ak at the kth decimal place. Thus, В is not counted in A1, A2,.... This shows that С cannot have a one to one correspondence with N or, in other words, С is not enumerable. The cardinal number с of the set С defined as above was called the "power of the continum" by Cantor. He denoted this by and called it "aleph one". Is it possible to find an infinite set P which has a magnitude bigger than and smaller than с which is the cardinality of С described above?

2 we had a square divided into nine tiny squares. How many triplet cubes-in-a-row do we have? 3, we have used rectangular coordinate axes OX,OY and OZ to identify the directions of the edges of the main cube. Taking the slices parallel to the OXY plane, we have three sets of nine tiny cubes. 2, with eight sets of 3 tiny cubes in a row. So in three slices we have 3 x 8 = 24 such sets. Now look at the slices parallel to the OYZ plane. Here too you will have 24 sets of 3 triplet cubes. But not all of them are new.