Some Frequently Used Symbols in Mathematics

is an element or member
of the set

is not an element of

implication
p  q is read ‘ if p, then q’

if and only if
p  q is read ‘ p if and only if q’

for all
‘ x’ is read as ‘for all x’

there exists
‘ x’ is read as ‘ there exists an x’

there does not exist
!
there exists uniquely

such that

approximately equal to

therefore

the empty set
Note: This is not a zero or an O
{x | …}
Set builder notation
read as ‘the set of all x such that …
??
what the bleep
what are you doing? Hello! Say something.
 JDarck 2005
‘x  R’ reads as ‘x is an element of the Real numbers’
‘! x’ is read as ‘ there exists a unique x’
‘ x  x  R’ reads as ‘for all x such that x is an
element of the Real numbers’
‘e  2.718281828459’ reads ‘‘e’ is approximately equal
to the rational number 2.718281828459’