Nine Zulu Queens Ruled China

"Nine Zulu Queens Ruled China" is a mnemonic for the groups of numbers, starting with the smallest, the natural numbers (represented by a hollow `N`).

`N` stands for `Natural` and the natural numbers are all the positive integers (1, 2, 3, ...). These are used to count items, e.g., 5 boys and 2 girls. You can`t have "half a boy" or "a minus girl": the `object-counting` numbers are the natural numbers. Note: some mathematicians consider 0 to also be a natural number.

`Z` stands for `Zahlen`, the German word for integers (..., -2, -1, 0, 1, 2, ...). These are the positive and negative integers. Notice that the naturals are a part of this group, hence this is the next babushka in order of size, inside of which is the natural numbers.

`Q` stands for `Quotient`, i.e. a/b, where a and b are integers. Therefore, this is the group of all rational numbers. Now, numbers may be used for things other than counting, and decimals may be used where needed.

`R` stands for `Real`, which is all the numbers without an imaginary part (numbers excluding those with added multiples of root -1). This is all the rational numbers, plus all the irrational numbers.

`C` stands for `Complex`, which is all the numbers. All numbers can be expressed in the form real part + imaginary part, hence all numbers are `complex`. E.g., 2 is complex because 2 = 2 + 0i. It being real, rational, integral, and natural doesn`t prevent it from being complex too. 2 is one of the numbers in the centre of the babushka. However, a number such as 12 + 11i is only in the final layer of the babushka, as it is not real, therefore not rational, integral, or natural.

Many non-mathematicians use the existence of complex numbers to argue that mathematicians just invent stuff when it suits them, e.g. when it proved impossible to square root a negative number, new maths was invented so that now it was possible. Lewis Carroll, the author of Alice in Wonderland and a mathematician at Christchurch, Oxford, was also against imaginary numbers, even dedicating part of a speech by the Mad-Hatter to mock their existence. Nowadays however, complex numbers are used in representing electromagnetic waves and electric currents and are essential in the field of electronics.

Exercise for the reader: as there are infinitely many naturals, and there are more integers than naturals, how many integers are there? Then how many rational numbers are there?... (this maybe is more suited as food for thought than something for pen and paper)