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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-setformatting Text-onlyformatting 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-BA U B` If you don't spell out the set union, define your notation. `A-intersect-BA ^ B` If you don't spell out the set intersection, define your notation.. `A-subset-BA < B` If you don't spell out the subset relation, define your notation. `A-subset or equal-BA <= 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. `Rthe real numbers` If you use "R" for "the set of all real numbers", define the notation. Otherwise, spell out the set you mean. `Qthe 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. `Cthe 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 setØ` 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-complementA^c` Either spell out the complement relation, or define "to the power c" as being "complement". `A-complement-BA - B` Either spell out the complement relation, or define "subtraction" to mean "complementation". `a is in Aa-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 Aa-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". `iffif 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. `vor` 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.

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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 [Date] [Month] 2016

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