Cambridge O Level Mathematics D (4024)
This chapter would be quite long and might get boring at times as you might know most of these things. I would rather suggest you to go thoroughly through the number system and give the rest of the chapter a quick read and update your what you've learned if you find anything unfamiliar.
Number systems:
Definitions of different types of numbers we use:
- Natural numbers: Natural numbers are counting numbers. Natural number include whole numbers only, however, it may or may not include 0 (zero). Natural numbers only include positive numbers. E.g. {1, 2, 3, 4, 5,...}.
- Whole numbers: All non-fractional numbers are called whole numbers. It includes zero. E.g. { 0, 1, 2, 3, 4,...}. Any number like 0, 7, 212, 1023 are all whole numbers.
- Integers: Integers include all negative and positive non-fractional numbers (or whole numbers) and 0 (zero). E.g. {...-3, -2, -1, 0, 1, 2, 3,...}
- Rational numbers: Rational numbers are all numbers that can be expressed as a ratio or a fraction. This would be possible if both the numerator and denominator are whole numbers or more specifically integers. E.g. { 9.0, 8/1, 2/3, 0.55555} are examples of rational numbers. NOTE: If you put 2/3 in a calculator, you would get the number 0.66666666 and it would go on forever. These are also rational numbers and are expressed using a recurring decimal. A recurring decimal is a decimal number that has digits that repeat forever.
- Irrational numbers: An irrational number is a number that cannot be expressed as a fraction. This is because in these numbers, there is not a finite number of numbers when written as a decimal. Instead, the numbers go on forever without repeating. Hence, these numbers can't either be expressed using a recurring decimal. E.g. { √2 = (1.41421356…), π = (3.14159265…)}
- Real numbers: A real number is any quantity on the number line. It includes all of the types of numbers mentioned above. E.g. {0, 1, 2, 2.5, 2/3, √2, π}. (√(−6), negative root of something is NOT a real number).
- Imaginary number: An imaginary number is a number which is not a real number. E.g. Negative root of something (√(−6)).
