Set-theory and logical statements generally have their own notation.
While these topics do not properly belong within the subject of algebra, their notation often arises
in algebra courses.
Type-set formatting
Text-only formatting
Notes
(2, 3)
(2, 3)
Put points in parentheses. Square brackets or other notation
(or nothing at all) has other meaning.
(2, 3)
(2, 3)
When you are writing an open interval, use parentheses, and
note that "this is an interval", to differentiate an interval from a point.
[2, 3]
[2, 3]
Use square brackets to indicate closed intervals.
[2, inf.) [2, infinity)
For "infinity", either spell out the word or else
abbreviate as "inf.". Do not try to approximate the infinity symbol with two lower-case
O's. Never use a square bracket at infinity, by the way. "Infinity" is not a number,
so you can't "include" it in the interval.
A-union-B A U B
If you don't spell out the set union, define your notation.
A-intersect-B A ^ B
If you don't spell out the set intersection, define your notation..
A-subset-B A < B
If you don't spell out the subset relation, define your notation.
A-subset or equal-B A <= B
If you don't spell out the subset relation, define your notation.
A-not a subset-B
Spell out this relation.
{1, 2, 3}
{1, 2, 3}
Sets are customarily written using curly braces.
N {1, 2, 3,...} the natural numbers
If you use "N" for "the set of natural numbers",
tell the tutor what you mean.
Z {..., -1, 0, 1, 2,...} the integers
If you use "Z" for "the set of integers, tell
the tutor what you mean. Otherwise, spell out the set you mean.
R the real numbers
If you use "R" for "the set of all real numbers",
define the notation. Otherwise, spell out the set you mean.
Q the rationals
If you use "Q" for "the set of all rational
numbers" (that is, the set of all fractions), define the notation. Otherwise, spell
out the set you mean.
C the complex numbers
If you use "C" for "the set of all complex
numbers", define the notation. Otherwise, spell out the set you mean.
{} the empty set Ø
Curly braces are commonly used to denote sets, so you can
use curly braces with nothing between to denote the empty set. Or (on a PC) hold down the
"ALT" key and type "0216" on the numeric keypad.
A-complement A^c
Either spell out the complement relation, or define "to
the power c" as being "complement".
A-complement-B A - B
Either spell out the complement relation, or define "subtraction"
to mean "complementation".
a is in A a-element of-A
The "is an element of" symbol is a tough one. Do
not try to approximate it using a capital E; I've never seen anyone understand what that
meant. Just spell out the relationship.
a is not in A a-not an element of-A
Spell out the relation.
if (this) then (that) ==>
Either spell out the "if-then" relation, or approximate
the arrow using two "equals" signs, to differentiate "if-then" from "greater
than or equal to".
iff if and only if <==>
The abbreviation "iff" for "if and only if"
is fairly standard and should be recognized in context, but spell things out, if you're not
sure.
there exist
Don't try to fake this symbol. Just spell out your meaning.
for all
Don't try to fake this symbol. Just spell out your meaning.
^ and
In the context of a logical statement, the carat should be
recognized as meaning "and", but spell things out if you're not sure.
v or
Using "v" for the "or" symbol could be
confusing, so either spell out your meaning or clearly define what you mean by "v".
~
~ ! not
There are various symbols for "not", so define your
notation, no matter which you use.
Stapel, Elizabeth. "Formatting Math as
Text: Set and Logical Notation." Purplemath. Available
from http://www.purplemath.com/modules/mathtext2.htm.
Accessed
