Signs of Comparison - Part 2

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.

1. 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.

   Pointing-Right Over Pointing-Left
   Pointing-Right Over Pointing-Left
   Pointing-Left Over Pointing-Right
   Long Pointing-Right Over Short Pointing-Left
   Short Pointing-Right Over Long Pointing-Left
   Pointing-Right With Upper Barb Only Over Pointing-Left With Lower Barb Only
   Pointing-Left Over Boldface Pointing-Right
   Boldface Pointing-Right Over Pointing-Left
   Boldface Pointing-Left Over Pointing-Right
   Boldface Pointing-Right Over Boldface Pointing-Left
   Boldface Pointing-Left Over Boldface Pointing-Right

   1. 
      

   2. 
      

2. Equals:
   

   Horizontal Bar	-
   Oblique Stroke	/or\
   Equals Sign	=

   As shown in c through k below, a single horizonal bar, an oblique stroke, or an equals sign may appear as part of a sign of comparison compounded vertically. The horizontal bar or oblique stroke is often substituted for the equals sign.

3. 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)

   1. 
      

   2. 
      

   3. 
      

   4. 
      

Bar Over Inclusion
Equals Sign Over Inclusion
Bar Under Inclusion
Equals Sign Under Inclusion

Bar Under Intersection
Equals Sign Under Intersection

f. Less Than:

Bar Over Less Than (is equal to or less than)
Equals Sign Over Less Than (is equal to or less than)
Bar Under Less Than (is less than or equal to)
Equals Sign Under Less Than (is less than or equal to)

Bar Over Logical Product
Bar Over and Bar Under Logical Product
Bar Over and Equals Sign Under Logical Product
Bar Under Logical Product
Equals Sign Over Logical Product
Equals Sign Over and Bar Under Logical Product
Equals Sign Over and Equals Sign Under Logical Product
Equals Sign Under Logical Product

Bar Over Logical Sum
Bar Over and Bar Under Logical Sum
Bar Over and Equals Sign Under Logical Sum
Bar Under Logical Sum
Equals Sign Over Logical Sum
Equals Sign Over and Bar Under Logical Sum
Equals Sign Over and Equals Sign Under Logical Sum
Equals Sign Under Logical Sum

Bar Over Reverse Inclusion
Equals Sign Over Reverse Inclusion
Bar Under Reverse Inclusion
Equals Sign Under Reverse Inclusion

j. Tilde:

Bar Over Single Tilde
Equals Sign Over Single Tilde
Double Tilde (is approximately equal to)
Bar Under Double Tilde
Equals Sign Over Double Tilde
Bar Under Single Tilde
Equals Sign Under Single Tilde (is congruent to)
Bar Under Double Tilde
Equals Sign Under Double Tilde

Bar Over Union
Equals Sign Over Union

Signs of Comparison Compounded Horizontally: When two or more sign of comparison are arranged side by side, the combination becomes a single comparison sign compounded horizontally. The multipurpose indicator must be placed between the unspaced symbols to indicate that they are printed horizontally, not vertically. Unlisted signs of comparison compounded horizontally must be transcribed according to the same principle.

1. Arrows:

   Pointing-Up Followed by Pointing Down
   Pointing-Down Followed by Pointing-Up
   Pointing-Up Followed by Boldface Pointing-Down
   Pointing-Down Followed by Boldface Pointing-Up
   Boldface Pointing-Up Followed by Pointing Down
   Boldface Pointing-Down Followed by Pointing-Up
   Boldface Pointing-Up Followed by Boldface Pointing-Down
   Boldface Pointing-Down Followed by Boldface Pointing-Up

   1. 
      

2. Greater Than:
   

   Followed by Less Than
   Followed by Equals Sign Followed by Less Than

   1. 
      

   2. 
      

3. Less Than:
   

Followed by Greater Than
Followed by Equals Sign Followed by Greater Than

Negated Signs of Comparison: In print, a sign of comparison may be negated by a vertical line of by a slant line drawn through it. In braille, the symbol must be used to represent either of the print negation signs and must be placed immediately before the sign of comparison being negated. Negated signs of comparison not illustrated below must be transcribed according to the same principle.

Signs of Comparison and Boldface Type: When it is necessary to show that a sign of comparison is printed in boldface type, dots 4-5-6 are placed before the corresponding symbol in braille. However, the use of dots 4-5-6 to denote boldface type is restricted to the specific signs listed below. They must not be used with any other sign of comparison. Boldface signs of comparison should be used only when the distinction between the regular and boldface forms of the same sign has mathematical significance.

Boldface Arrows

Boldface Equals = 

1. shows that the reaction begins at the left and is completed to the right.
   

2. a X c = b X d if and only if a = c and b = d.