2013年9月21日星期六

Drawer principle

Principle 1: Put more than n objects into n-drawer, then at least one drawer in less than two.
Reference (contradiction): If each object into a drawer at best, the maximum total number of objects is n, rather than title set n + k (k ≥ 1), it is not possible.
Principle 2: Put more than mn (m times n) of n objects into a drawer, then at least one drawer of not less than m +1 objects.
Proof (reductio ad absurdum): If each of m objects into the drawer up, then up into the Magnetic Grate n mn of objects, with the title set does not match, it is impossible.
Principle 3: infinitely many pieces of objects into n drawers, at least one drawer with an infinite number of objects.
Principle 1, 2, 3 are schematic representation of the first drawer.

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