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Formatting Math as Text (page 2 of 4)

Sections: Common algebra notation, Set and logical notation, Other math notation, Notes on posting


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.

the interval [2, infinity)

[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-union-B
A U B

If you don't spell out the set union, define your notation.

A-intersect-B

A-intersect-B
A ^ B

If you don't spell out the set intersection, define your notation..

A-subset-B

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

A-not a subset-B

Spell out this relation.

{1, 2, 3}

{1, 2, 3}

Sets are customarily written using curly braces.

the natural numbers

N
{1, 2, 3,...}
the natural numbers

If you use "N" for "the set of natural numbers", tell the tutor what you mean.

the set of integers

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.

the real numbers

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.

the rational numbers

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.

the complex numbers

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

{}
the empty set

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-complement
A^c

Either spell out the complement relation, or define "to the power c" as being "complement".

A-complement-B

A-complement-B
A - B

Either spell out the complement relation, or define "subtraction" to mean "complementation".

a-element of-A 

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-not an element of-A 

a is not in A
a-not an element of-A

Spell out the relation.

if-then

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".

if-and-only-if

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 exists

there exist

Don't try to fake this symbol. Just spell out your meaning.

for all

for all

Don't try to fake this symbol. Just spell out your meaning.

and

^
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.

or

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.

Notes on posting   Copyright Elizabeth Stapel 2006-2008 All Rights Reserved

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Cite this article as:

Stapel, Elizabeth. "Formatting Math as Text: Set and Logical Notation."
    Purplemath. Available from 
http://www.purplemath.com/modules/mathtext2.htm.
    Accessed
 

 



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