Key Points
1. When solving a problem it is often helpful to follow these steps:
• Solve similar but simplified versions of the same problem.
• Look for patterns in your results.
• Form a conjecture so that you can predict what would happen in more complicated cases.
• Check that your prediction are correct.
• Express your conjecture in general form, using algebra if appropriate.
• Prove your conjecture.

2. Types of numbers:
• Counting Numbers - Z+ - positive whole numbers (1, 2, 3...).
• Natural Numbers - N - Counting numbers and zero (0, 1, 2, 3...).
• Integers - Z - All whole numbers: (-2, -1, 0, 1, 2...).
• Rational Numbers - Q - m ⁄ n where m and n are integers (n ≠ 0) e.g. 2 ⁄ 3, -15 ⁄ 7.
• Real Numbers - R - Rational and irrational numbers e.g. π, (√3 + 6), -5 ⁄ 7, 6.

3. ⇒ means 'implies', 'if... then...', 'therefore'.
⇐ means 'is implied by', 'follows from'.
⇔ means 'implies and is implied by', 'is equivalent to'.

The converse of A ⇒ B is A ⇐ B.
If A ⇐ B, A is a necessary condition for B.
If A ⇒ B, A is a sufficient condition for B.

4. Methods of proof:
• deduction
• exhaustion
• contradiction

5. Methods of disproof:
• contradiction
• deduction

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