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Mathematical Proof

A statment that has been proven is called a theorum.

A statment that has yet to be proven is called a conjecture

Example of proof

Statment: The product of two odd numbers is always odd

Demonstration: \(5\) x \(7 = 35\), which is odd

Proof: \(x\) and \(y\) are integers, therefore \((2x+1)\) and \((2y+1)\) are both odd integers
\(\((2x+1)(2y+1) = 4xy+2x+2y+1\)\)
\(\(=2(2xy+x+y)+1\)\)
Since x and y are integers, 2xy+x+y is also an integer
So \(2(2xy+x+y)+1\) is one more than an odd number
So the product of two odd numbers is odd

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