Simple Proof 1
Simple proof of odd and even numbers.
It is the eventual academic aim of all subjects to further human knowledge by being able to prove something is true. In mathematics, we can use various mechanisms to do this. Almost all these mechanisms mean that you have to take a general view of the subject (in other words, use algebra) as opposed to providing individual examples. The individual examples can be useful though as they often provide clues as to how you may to choose to tackle the general cases.
The one exception to this is disproving something by counter example. Here, you just have to provide one example where something is not true in order to disprove any given hypothesis.
Mathematics is fantastic as you will grow to learn. It is pretty much the only subject where you can prove something by picking up a pen and a piece of paper and engaging you brain.
Proof involves studying the following:
Simple proof of odd and even numbers.
Proof by deduction is where you use something that you already know in order to generalise a proof. Here, I run from a simple multiplication trick to see if it can be built into more general terms and hence become a proof which will work for any number.
Proof by exhaustion is where you have to look at various cases and prove each one in turn. Cases might include what if the number is odd, even, zero, negative or a fraction.
Proving something isn't true is often a lot easier than proving it is true. All you have to do is find one example where it does not work. Then you have done it.