This Ted Talk, shared at The Scholarly Kitchen by David Crotty, tells us about the origins of our numbering system.

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The representation of these digits in type can be done in two ways: old style and lining. Old style figures extend up and down from the x-height, unlike the lining figures shown in this typeface: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, which are of uniform height. I prefer old style (though they should never be used in mathematical setting), and find it slightly disconcerting that when I draft a piece in this WordPress blog the numerals show as old style, whereas they will actually be displayed in a different, sans serif font. Here’s the draft of this paragraph: As far as I am aware almost all sans serif fonts just have modern numbers. The only exceptions I can find are Maxima and ITC’s Goudy Sans which provide both modern and old style. Optima, a sort of serify* sans serif face also has both. Here are both sets in Goudy Sans. Number: “The precise sum or aggregate of a collection of individual things or persons; the quantity or amount”

Numeral: “a word expressing or denoting a number”

Digit: “A whole number less than ten: any of the nine or (including zero) ten Arabic numerals representing these”

Natural numbers: 1, 2, 3, 4, 5, . . . all the way “to infinity and beyond”

Whole numbers: 0, 1, 2, 3, 4, 5, . . . Like Natural but including zero

Integers: . . . -3, -2, -1, 0, 1, 2, 3, 4, 5, . . . Like Whole Numbers but including negative numbers too

Rational numbers: All of the above but including fractions, decimals which end, and decimals which repeat or have a pattern

Irrational numbers: Decimals which never end, like √37 and π

Perfect number: A number the sum of whose factors, excluding the number itself, is exactly equal to the number itself

Abundant number:  Same story, but with a total greater than the number itself (e.g. 18)

Deficient number: Same story, but totaling less than the number itself (e.g. 8)

Amicable numbers: If the sum of the factors of a = b, and the factors of b = a, the numbers are amicable (e.g. 220 and 284)

Cardinal number: “A number which answers the question ‘how many?” As opposed to

Ordinal number: Marking position in an order or series: first, second etc.

Nominal number: A number used to identify someone or thing (e.g. Social Security Number, or 10 on Harry Kane’s back)

Prime number: A natural number greater than 1 with no factors

Composite number: A natural number which has more than two factors

Directed number: A number which is either negative or positive. (Zero is neither negative nor positive)

Imaginary number: The square root of a negative number

Transfinite numbers: Cardinal numbers indicating the size of infinite sets

Real number: a number that can be located on a number line

Complex number: A member of the most general or inclusive set of numbers used in algebra: a number that can be expressed in the form a + bi, where a and b are real numbers and i = √-1

Number complex: the compulsion to list all these crazy definitions.

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* Optima has swellings at the top and bottom of verticals which to my eye make it a sort of transitional face between serifed and sans serif, although it is really a sans serif face. 