BRL: Braille through Remote Learning

Specialized Codes Course



Session Topics
  • Fractions and Fraction Indicators
  • Radicals and Radical Indicators
  • Format
  • Roman Numerals
  • Signs of Operation
  • Reference Symbols

  • Writing Exercise

    Other Resources
  • Contact instructor
  • Send mail to class
  • Main BRL page
  • Contractions Lookup
  • Contractions List
  • Intro Braille course
  • Transcribers course

  • Signs of Operation

    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+dots 3-4-6
    Minus-dots 3-6
    Multiplication:   Cross
    (Cartesian product)
    xdots 4dots 1-6
    Multiplication: Dotdots 1-6
    Division (divided by) dots 4-6dots 3-4
    Plus or Minus±dots 3-4-6dots 3-6
    Minus or Plusdots 3-6dots 346
    Plus Followed by Minus+-dots 3-4-6dots 5dots 3-6
    Minus Followed by Plus-+dots 3-6dots 5dots 3-4-6
    Minus Followed by Minus--dots 3-6dots 5dots 3-6
    Fraction Lines (over, divided by):
    Horizontal Simple Fraction Line
    ____dots 3-4
    Fraction Lines (over, divided by):
    Diagonal Simple Fraction Line
    /dots 4-5-6dots 3-4
    Fraction Lines (over, divided by):
    Horizontal Complex Fraction Line
    ___dots 6dots 3-4
    Fraction Lines (over, divided by):
    Diagonal Complex Fraction Line
    /dots 6dots 4-5-6dots 3-4

    Additional Signs of Operation:

    1. Ampersand
      (and, logical conjunction):
      & dots 4-5-6dots 1-2-3-4-6

      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.

      1. A & B

      2. The & denotes logical conjunction.

      3. AT&T

      4. The B & O Railroad.

    2. Asterisk * dots=4dots 3-4-5-6
      Crosshatch-number sign,
      tic-tac-toe, pounds (weight)
      # dots 4-6dots 3-4-5-6
      Paragraph Mark dots 4dots 6dots 1-2-3-4
      Section Mark § dots 4dots 6dots 2-3-4

      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.

      1. f * g

      2. (1 + 2) * (3 + 4)

      3. 1 * 2

      4. .1 * .2

      5. x* > x

      6. A'*

      7. x # y = y # x

      8. 1 # 2 = 2 # 1

      9. In R#, # denotes a 1-place operation symbol.

      10. A ¶ B

      11. 3 ¶ 4 = 4 ¶ 3

      12. A ¶ B

      13. 3 § 4 = 4 § 3

    3. Back Slash
      (divides, is a factor of):
      \ dots 4-5-6dots 1-6

      1. b\a can be read as "b divides a".

        3\6 denotes "3 is a factor of 6".

    4. Dagger:
      Single dots 4-5-6dots 1-6
      Double dots 4-5-6dots 4-5-6dots 1-2-4-5-6

      1. AB = BA

      2. AB = BA

    5. Dot (and, times): dots 1-6

      The dot may be used as a multiplication sign or to denote "and."

    6. Hollow Dot: dots 4-6dots 1-6

      The hollow dot may be used as a sign of operation or as a superscript to represent degrees of temperature or angle.

    7. Intersection (cap): dots 4-6dots 1-4-6

    8. Logical Product (and, meet): dots 4dots 1-4-6

    9. Logical Sum (or, join): dots 4dots 3-4-6

    10. Minus With Dot Over
      (proper difference):
      dots 4dots 3-4-6

      1. x y = 0

      2. x y' = pd(x y)

    11. Tilde (not):
      Simple ~ dots 4dots 1-5-6
      Extended dots 4dots 6dots 1-5-6

      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 dots 4 must be inserted between them to indicate that they are written horizontally.

      1. s V t

    12. Union (cup): dots 4-6dots 3-4-6

    13. Vertical Bar (is a factor, divides): | dots 1-2-5-6

      The vertical bar is used both as a sign of grouping and as a sign of operation.

      1. In b | a, b is a factor of a.

      2. 6 | 12 can be read as "6 divides 12."

      3. x + 2 | x2 + 7x + 10

    14. Vertical Bar Negated
      (does not divide):
      dots 1-2-5-6

      1. 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 4-5-6 followed by the appropriate sign of operation. In this case, dots 4-5-6 must be considered not as the boldface type-form indicator but as part of its related symbol. Dots 4-5-6 must not be used with any other sign of operation.

      Boldface Plus+dots 4-5-6dots 3-4-6
      Boldface Minus-dots 4-5-6dots 3-6
      Boldface Plus Followed by
      Boldface Minus
      +-dots 4-5-6dots 3-4-6dots 5dots 4-5-6dots 3-6
      Boldface Plus Followed by
      Regular Minus
      +-dots 4-5-6dots 3-5-65dots 3-6
      Regular Plus Followed by
      Boldface Minus
      +-dots 3-4-6dots 5dots 4-5-6dots 3-6
      Boldface Minus Followed by
      Boldface Plus
      -+dots 456dots 3-6dots 5dots 4-5-63dots 4-6
      Boldface Minus Followed by
      Regular Plus
      -+dots 4-5-6dots 3-6dots 5dots 3-4-6
      Regular Minus Followed by
      Boldface Plus
      -+dots 3-6dots 5dots 4-5-6dots 3-4-6

      1. a + b = b + a

      2. a + - c = b - + d

    Developed by
    Shodor logoThe Shodor Education Foundation, Inc.
    in cooperation with the
    North Carolina Central University
    and the Governor Morehead School for the Blind

    Copyright © 1998