Proof
| Mathematics is a very precise language. When mathematicians lay out a logical argument for why something is true, they are giving a proof. A proof is based on deductive reasoning showing that there are no instances in which the theorem or other statement can be false. The process of proving a theorem involves identifying the given information, and showing step-by-step reasons to reach a logical conclusion. |
Informal Proof
| When you give reasons for something being true, but don’t necessarily argue it step-by-step, you are giving an informal proof. |
Generally, informal proofs are used by mathematicians to show that a more formal proof is possible.
Example
The following is a simple algebraic example of an informal proof.
Given 3x + 2 = 11, Prove x = 3
3x = 9
x = 3
A mathematician would be able to follow the argument enough to be able to construct a formal proof.
Formal Proof
| A formal proof is much more precise and leaves no doubt as to the logical conclusion. Reasons are given for each step in a formal proof. |
Example
Using the same example, we could write a more formal proof in paragraph form.
Given 3x + 2 = 11, Prove x = 3
You can subtract 2 from both sides because of the subtraction property of equality. This leaves 3x = 9. Then, you can divide both sides by 3 because of the division property of equality. Thus, x = 3.
