Review of Signs of Comparison: A space must be left before and after a sign of comparison. However, no space should be left between a sign of comparison and a sign of grouping, a braille indicator, or a punctuation mark which is related to it.
The following simple signs of comparison have already been introduced:
Arrow 
Pointing Left 


Pointing Right 
Contracted Form 


Uncontracted Form 



Pointing Left and Right 


Pointing Up 


Pointing Down 


Pointing Up and Down 



Equals 
=

Greater Than (is greater than) 
With Straight Sides 


With Curved Sides 



Less Than (is less than) 
With Straight Sides 


With Curved Sides 



Proportion (as) 
::

Ratio (is to) 
:

Additional Signs of Comparison:
 Arc
Concave Upward 

Concave Downward 

 Equivalence (is equivalent to):
 Identity (is identical to, is congruent to):
This symbol must not be used for is congruent to if another sign is used for this purpose in print.
 Inclusion (is contained in, is a subset of):
 Membership (is an element of, belongs to):
This symbol is generally used for sets and their elements. It must not be mistaken for the Greek uncapitalized epsilon even though it may be referred to as such.
 Parallel To (is parallel to): 
 AB  CD
 Perpendicular To (is perpendicular to):
 Relation (is related to): R
When an R or any other letter or sign is used between two expressions to show relation, the letter or other symbol must be treated as a sign of comparison.
 a R b
 Reverse Inclusion (contains;in logic, implies):
 Reverse Membership (contains the element):
 Tilde
Simple (is related to, is similar to): 


Extended (is related to): 


The tilde may be used as a sign of operation or as a sign of comparison.
 Variation (varies as):
 Vertical Bar (such that): 
The vertical bar may be used as a sign of grouping, as a sign of operation or as a sign of comparison. When used as a sign of comparison, it usually occurs in an expression within braces used for set notation. However, it may also appear in other situations.
 {x  x has the property T}
 {w  w = w + 1}
 {m  3 (m  6) = 9}
 {(x,y)  x + y = 6}
Signs of Comparison Compounded Vertically: When two or more simple signs of comparison are arranged one under the other, the combination becomes a single comparison sign compounded vertically. The symbol for the uppermost sign must be written first and unspaced from the symbol for the next lower sign.
 Arrows: When a right pointing arrow in regular type with a full barb and single shaft of ordinary length is part of a sign of comparison compounded vertically, its contracted form must not be used.
PointingRight Over PointingLeft 


PointingRight Over PointingLeft 


PointingLeft Over PointingRight 


Long PointingRight Over Short PointingLeft 


Short PointingRight Over Long PointingLeft 


PointingRight With Upper Barb Only Over PointingLeft With Lower Barb Only 


PointingLeft Over Boldface PointingRight 


Boldface PointingRight Over PointingLeft 


Boldface PointingLeft Over PointingRight 


Boldface PointingRight Over Boldface PointingLeft 


Boldface PointingLeft Over Boldface PointingRight 


 Equals:
Horizontal Bar 
 

Oblique Bar 
/or\ 

Equals Sign 
= 

As shown in c through k below, a single horizonal bar, an oblique bar, or an equals sign may appear as part of a sign of comparison compounded vertically. The horizontal bar or oblique bar is often substituted for the equals sign.
 Greater Than:
Bar Over Greater Than (is equal to or greater than) 


Equals Sign Over Greater Than (is equal to or greater than) 


Bar Under Greater Than (is greater than or equal to) 


Equals Sign Under Greater Than (is greater than or equal to) 


Go to Signs of Comparison, Part 2
