The Naming of Sets in Set Theory:

The Naming of Sets in Set Theory

Figure 1:  I drew this set-naming italic character in SVG.  You may view the code of this image at my Codepen Account.

Figure 2: What the SVG image looks like when exported as a PNG.[1]

In Set Theory - which underpins so much of computing mathematics - we conventionally name sets with capital italic letters.

In computer science, a name such as:

A

, would be termed an:

‘identifier’

. In the below example, we shall use the capital italic character:

R

so as to name the members of the set of Radix-ten [2] integers.

Figure 3: “A SQUARE-ROOT SIGN  This sign is from radix (Latin for root) and was first used by Leonardo da Pisa in 1220.  Today’s √ sign, which may be a distortion of the letter “r”, is sixteenth-century German.”[3]

An Example of Naming a Set with an Italic

Italic Capital Character:

Let:

R

equal the set of radix-ten integers:

R = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

. In the above example, the integers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

are termed ‘elements.’ The integers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

are considered elements of the set of radix-ten integers.


[1] An acronym that is sometimes pronounced “ping” /pɪŋ/.  The acronym stands for ‘portable network graphics.’

[2] The Latin feminine third-declension noun, ‘rādīx, rādīcis’ means ‘root.’ The Latin phrase, ‘in rādīce,’ means ‘at root.’ The ten unique symbols - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 - that we use to express quantities in base-ten are at the root of all denary numbers; at the root of all decimal numbers; at the root of all decimal numbers; at the root of all base-ten numbers; are at the root of all radix-ten numbers;

[3]Life Science Library: Mathematics, (Time-Life International (Nederland) : 1963, 1965, revised 1972), David Bergamini, p. 49.

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