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We all know what numbers are 1, 2, 3, 4, 5, etc. including negative numbers -1, -2, -3, -4, -5, etc. But did you know that mathematicians classify numbers into different types; into a number system? Let’s start at the top with real numbers. They can be positive, negative, zero, decimals, fractions, pi. Nearly any number you can think of is a real number. Only imaginary numbers, like the square root of -1 and infinity, aren’t real, but we don’t really need to worry about them at this stage. If you can put the number on a number line, then it’s a real number. This symbol is used to represent Real Numbers. Real numbers split into two subsets: rational and irrational numbers. I just remember rational fractional sound similar. So any whole number, such as terminating decimals, recurring decimals. In fact, all numbers, except for non-repeating decimals, are rational. Decimals that do not repeat are irrational. Some well-known examples are pi,e and Square root 2.
Many square roots, cube roots, etc are irrational. If the decimal places go on forever without repeating, they are irrational.
Now back to rational numbers. These can be separated down further to natural numbers and integers. Integers are any positive whole numbers, negative whole numbers, zero. Whereas natural numbers are just from 0 and the positive numbers.
Strangely there is no general agreement amongst mathematicians about whether to include 0 in the natural numbers or not. Sometimes 0 is included, sometimes it isn’t. If 0 isn’t considered a natural number, then a whole new category is needed, called whole numbers. Which is exactly the same as natural numbers but also includes the 0. So there we have the real number system. The number 1, for example, is a natural number, a whole number, integer, rational number, and a real number.
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