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