Our instructor in his desire to convince the novices of the paradoxical character of chess set the following position on the board at one of the first sessions.

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From the defects in the basic theory of present classical infinite theory, the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of is analyzed and a mysterious error is found:The core of Cantor's above two important proofs in set theory are actually another versions of Russell's paradox and the very same paradoxical idea was applied in both Russell and Cantor's work, and Cantor made wrong use of this paradox idea with two logical mistakes.

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