# Mathematical Operators

! ("bang", aka "exclamation point"); ASCII: `33`, Unicode: `U+0021`, HTML: `&#33;`

1. Factorial: `x!` denotes the factorial of `x`, which denotes the product of `x` and all positive integers less than `x`. For example, `4! = 4 × 3 × 2 × 1 = 24`.
2. Negation: in logical notation `!x` is typically read as "not x", meaning the opposite of `x`. For example, if `x` is a true proposition, then `!x` is false. More commonly in CS papers, negation is indicated by the symbol `¬` [ref].

% ("percent sign"); ASCII: `37`, Unicode: `U+0025`, HTML: `&#037;`

1. Modulo operator: the remainder left after division, eg `65 % 7` is the remainder left after dividing 65 by 7 (in this case `65 % 7 = 2` because `65 = 7 * 9 + 2`) [ref]
2. Percentage: expresses a proportion as the numerator in x/100, eg 68% equals 0.68 [ref]

| ("pipe", aka "vertical bar"): ASCII: `124`, Unicode `U+007C`, HTML: `&#124;`

1. Absolute value: `|x|` denotes the distance of `x` from the origin (i.e. zero) (`|-3| = |3| = 3`) [ref]
2. Conditional probability: `(B|A)` can be read as "B given A" and `P(B|A)` often denotes "the probability of event B given that even A occurs." [ref]
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