Review of Signs of Operation: No space should be left before or after a sign of operation unless it is preceded or followed by a sign of comparison, an ellipsis, a dash, an unrealted word, or an abbreviation. However, no space must be left between an abbreviation and a fraction line. Signs of operation are mathematical symbols and must be punctuated accordingly.
The following signs of operation have already been introduced:
Plus  +  
Minus    
Multiplication: Cross (Cartesian product)  x  
Multiplication: Dot   
Division (divided by) 
 
Plus or Minus  ±  
Minus or Plus   
Plus Followed by Minus  +  
Minus Followed by Plus  +  
Minus Followed by Minus    
Fraction Lines (over, divided by): Horizontal Simple Fraction Line  ____  
Fraction Lines (over, divided by): Diagonal Simple Fraction Line  /  
Fraction Lines (over, divided by): Horizontal Complex Fraction Line  ___  
Fraction Lines (over, divided by): Diagonal Complex Fraction Line  /  
Additional Signs of Operation:
Ampersand (and, logical conjunction): 
& 

When the ampersand is used in mathematical context, it must be treated as a sign of operation and the symbol shown above must be used. However, when the ampersand is used in abbreviations or other literary context, the symbol and rules of English braille apply.
 A & B
 The & denotes logical conjunction.
 AT&T
 The B & O Railroad.
Asterisk 
* 

Crosshatchnumber sign, tictactoe, pounds (weight) 
# 

Paragraph Mark 
¶ 

Section Mark 
§ 

The asterisk, crosshatch, paragraph, and section marks must be represented by the symbols of Nemeth code; English braille symbols must not be used. If these signs of operation occur as superscripts or subscripts, their position must be shown.
The numeric indicator must be used before a numeral or a decimal point and a numeral following as asterisk, crosshatch, paragraph, or section mark.
 f * g
 (1 + 2) * (3 + 4)
 1 * 2
 .1 * .2
 x* > x
 A'*
 x # y = y # x
 1 # 2 = 2 # 1
 In R#, # denotes a 1place operation symbol.
 A ¶ B
 3 ¶ 4 = 4 ¶ 3
 A ¶ B
 3 § 4 = 4 § 3
Back Slash (divides, is a factor of): 
\ 

 b\a can be read as "b divides a".
3\6 denotes "3 is a factor of 6".
 AB = BA
 AB = BA
Dot (and, times): 


The dot may be used as a multiplication sign or to denote "and."
The hollow dot may be used as a sign of operation or as a superscript to represent degrees of temperature or angle.
Logical Product (and, meet): 



Minus With Dot Over (proper difference): 


 x y = 0
 x y' = pd(x y)
In logic, the tilde is used as a sign of operation meaning "not."
When two symbols for the tilde follow one another, the multipurpose indicator must be inserted between them to indicate that they are written horizontally.
 s V t
Vertical Bar (is a factor, divides): 
 

The vertical bar is used both as a sign of grouping and as a sign of operation.
 In b  a, b is a factor of a.
 6  12 can be read as "6 divides 12."
 x + 2  x^{2} + 7x + 10
Vertical Bar Negated (does not divide): 


 5 n
Signs of Operation and Boldface Type: The signs of operaiton listed below are to be used to show boldface type only when the distinction between the regular and the boldface forms of the same sign has mathematical significance. Each symbol consists of dots 456 followed by the appropriate sign of operation. In this case, dots 456 must be considered not as the boldface typeform indicator but as part of its related symbol. Dots 456 must not be used with any other sign of operation.
Boldface Plus  +  
Boldface Minus    
Boldface Plus Followed by Boldface Minus  +  
Boldface Plus Followed by Regular Minus  +  
Regular Plus Followed by Boldface Minus  +  
Boldface Minus Followed by Boldface Plus  +  
Boldface Minus Followed by Regular Plus  +  
Regular Minus Followed by Boldface Plus  +  
 a + b = b + a
 a +  c = b  + d
