= (the equals sign) means “is the same as” and was first introduced in the 1557 book The

Whetstone of Witte by Robert Recorde (c. 1510-1558).

< the less than sign mean “is strictly less than”, and > (the greater than sign) means

“is strictly greater than”. They first appeared in Artis Analyticae Praxis ad Aequationes

Algebraicas Resolvendas (“The Analytical Arts Applied to Solving Algebraic Equations”) by

Thomas Harriot (1560-1621), which was published posthumously in 1631.

the implies sign means “logically implies that”. (E.g., “if it’s raining, then it’s pouring” is

equivalent to saying “it’s raining ⇒ it’s pouring.”)

“it’s raining” implies the statement “it’s really humid” and vice versa.)

This notation “iff” is attributed to the great mathematician Paul R. Halmos (1916–2006).

the iff sign means “if and only if” and is used to connect logically equivalent statements.

(E.g., “it’s raining iff it’s really humid” means simultaneously that “if it’s raining, then it’s really humid”

“if it’s really humid, then it’s raining”. In other words, the statement

the universal quantifier symbol means “for all” and was first used in the 1935 publication

Untersuchungen ueber das logische Schliessen (“Investigations on Logical Reasoning”) by

Gerhard Gentzen (1909-1945).

the existential quantifier means “there exists” and was first used in the 1897 book Formulaire

de mathematiqus by Giuseppe Peano (1858-1932).