Basic Mathematical Symbols

Certain expressions are common in mathematics, and to save time in written work one should use the appropriate symbol for the expression. When reading the symbols out loud, use the full English expression. For example,

can be read ``for all a and b in the set of real numbers, a less than b implies a cubed is less than b cubed'' (or ``for all real numbers a and b, if a is less than b, then a cubed is less than b cubed'').

Written:   Spoken:
= for all (or ``for every'')
= there exists
= such that
= is orthogonal to (perpendicular to)
= intersection
= union
= is contained in
= is an element of
= is not an element of
= implies
= if and only if (or ``is equivalent to'')
= if and only if (same as above)
= less than
= greater than
= less than or equal to
= greater than or equal to
= the set of real numbers
= the set of natural numbers
= the set of integers
= the set of rational numbers
= the set of complex numbers