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.
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