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Category: Set Theory

Easy Induction Proof of Arithmetic Geometric Mean Inequality

July 3rd, 2009, No Comments

The Arithmetic-Geometric mean inequality says that If then and equality happens if and only if all ‘s are equal. The case for is trivial and for is equivalent to which is equivalent to . So the statement is true for . Now assume that the statement is true for . Without lost of generality we [...]

Principle of Countability

June 23rd, 2009, 2 Comments

Definition A set is is finite if there is a one-one correspondence between and the initial segment . A set is countably infinite if there is a one-one correspondence between and the set of natural numbers . A set is countable if it is finite or countably infinite. Before we start the discussion we need [...]

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