# Operators without Built‐in Meanings

When you enter a piece of input such as 2+2, the Wolfram Language first recognizes the + as an operator and constructs the expression Plus[2,2], then uses the builtin rules for Plus to evaluate the expression and get the result 4.

But not all operators recognized by the Wolfram Language are associated with functions that have builtin meanings. The Wolfram Language also supports several hundred additional operators that can be used in constructing expressions, but for which no evaluation rules are initially defined.

You can use these operators as a way to build up your own notation within the Wolfram Language.

The is recognized as an infix operator, but has no predefined value:
 In:= Out//FullForm= In StandardForm, prints as an infix operator:
 In:= Out= You can define a value for :
 In:= Now is not only recognized as an operator, but can also be evaluated:
 In:= Out= x⊕y CirclePlus[x,y] x≈y TildeTilde[x,y] x∴y Therefore[x,y] x↔y LeftRightArrow[x,y] ∇x Del[x] x Square[x] 〈x,y,…〉 AngleBracket[x,y,…]

A few Wolfram Language operators corresponding to functions without predefined values.

The Wolfram Language follows the general convention that the function associated with a particular operator should have the same name as the special character that represents that operator.

[Congruent] is displayed as :
 In:= Out= It corresponds to the function Congruent:
 In:= Out//FullForm= x \[name] y name[x, y] ∖[name] x name[x] ∖[Leftname] x,y,… ∖[Right name] name[x, y, …]

The conventional correspondence in the Wolfram Language between operator names and function names.

You should realize that even though the functions CirclePlus and CircleTimes do not have builtin evaluation rules, the operators and do have builtin precedences. "Operator Input Forms" lists all the operators recognized by the Wolfram Language, in order of their precedence.

The operators and have definite precedenceswith higher than :
 In:= Out//FullForm= xy Subscript[x,y] x+ SubPlus[x] x- SubMinus[x] x* SubStar[x] x+ SuperPlus[x] x- SuperMinus[x] x* SuperStar[x] x† SuperDagger[x] Overscript[x,y] Underscript[x,y] OverBar[x] OverVector[x] OverTilde[x] OverHat[x] OverDot[x] UnderBar[x]

Some twodimensional forms without builtin meanings.

Subscripts have no builtin meaning in the Wolfram Language:
 In:= Out//InputForm= Most superscripts are interpreted as powers by default:
 In:= Out//InputForm= A few special superscripts are not interpreted as powers:
 In:= Out//InputForm= Bar and hat are interpreted as OverBar and OverHat:
 In:= Out//InputForm= 