Mathematical Operators

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

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: %

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: |

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]