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Category: Simple Proof

Fundamental Theorem of Arithmetic

June 29th, 2009, No Comments

Fundamental Theorem of Arithmetic says that Every natural number has a unique prime factorization (up to some ordering). We’ll prove this by induction. Clearly has a unique prime factorization. Let assume that up to all numbers has a unique prime factorization. If is prime then we are done since itself is the prime factorization of [...]

More On Irrationality of Square Root

June 18th, 2009, No Comments

Theorem Square root of positive number of the form and are all irrational Proof The reference below proved this result in detail for the case , so let us here proof for the case . The other case will be left for the reader. Suppose in the lowest term. Then . Note that must be [...]

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