RULE XIX--SIGNS AND SYMBOLS OF OPERATION
About 95% of the expressions on this page are considered correct for the default MathSpeak settings, so some of the expressions do not yet adhere to the MathSpeak grammar.
Please refer to the Table of Contents page to find Rules that have been thoroughly modified and proofed.
Ampersand (and, logical product)
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verbose |
Ampersand |
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Asterisk
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verbose |
asterisk |
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Back Slash (divides, is a factor of)
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verbose |
backslash |
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Circle with Interior Dot
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verbose |
circled-dot |
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Circle with Interior Plus
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verbose |
circled-plus |
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Circle with Interior Minus
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verbose |
circled-minus |
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Dagger
- Single
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verbose |
dagger |
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- Double
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verbose |
double-dagger |
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Divison (divided by)
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verbose |
Division-sign |
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Dot (and)
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verbose |
dot |
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Fraction Line (over)
- Diagonal
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verbose |
Over
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- Simple
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verbose |
Over
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- Diagonal Complex
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verbose |
OverOver
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- Complex
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verbose |
OverOver
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- Hypercomplex
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verbose |
OverOverOver
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Hollow Dot
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verbose |
circle |
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Intersection (cap)
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verbose |
Intersection |
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Logical Product (and, meet)
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verbose |
Logical-and |
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Logical Sum (join, or)
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verbose |
Logical-or |
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Minus
- Regular
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verbose |
minus |
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- Boldface
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verbose |
Bold
minus |
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Minus Followed by Plus
- Boldface Minus Followed by Boldface Plus
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verbose |
Bold
minus Bold
plus |
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- Boldface Minus Followed by Regular Plus
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verbose |
Bold
minus plus |
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- Regular Minus Followed by Regular Plus
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verbose |
minus plus |
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- Regular Minus Followed by Boldface Plus
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verbose |
minus Bold
plus |
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Minus or Plus
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verbose |
minus-or-plus |
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Minus with Dot over (proper difference)
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verbose |
dotted-minus |
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Multiplication (times)
- Cross (cartesian product)
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verbose |
cross |
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- Dot
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verbose |
dot |
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Number Sign; Crosshatch; Tic-tac-toe; Pounds (weight)
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verbose |
Number-sign |
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Paragraph Mark
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verbose |
paragraph-mark |
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Plus
- Regular
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verbose |
plus |
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- Boldface
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verbose |
Bold
plus |
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Plus Followed by Minus
- Boldface Plus Followed by Boldface Minus
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verbose |
Bold
plus Bold
minus |
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- Boldface Plus Followed by Regular Minus
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verbose |
Bold
plus minus |
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- Regular Plus Followed by Regular Minus
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verbose |
plus minus |
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- Regular Plus Followed by Boldface Minus
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verbose |
plus Bold
minus |
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Plus or Minus
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verbose |
plus-or-minus |
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Section Mark
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verbose |
section-mark |
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Slash (per, over, divided by)
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verbose |
slash |
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Square
- Filled-In Square
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verbose |
filled-in-square |
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- Hollow Square
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verbose |
square |
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Star
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verbose |
figure-star |
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Tilde
- Extended
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verbose |
extended tilde |
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- Simple
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verbose |
tilde |
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Union (cup)
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verbose |
Union |
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Vertical Bar (is a factor, divides)
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verbose |
vertical-line |
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§129. Ampersand: When the ampersand is
used in literary context, and without reference to the specific nature of the
sign itself, it should not be regarded as a sign of operation, and accordingly,
the rules of English Braille apply. Otherwise, the symbol in the above list
must be used.
(1)
(literary context)
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verbose semantics |
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(2)

,! _& (t5 denotes logical
3junc;n4
(specific attention is called to the nature of the
sign)
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verbose semantics |
The Ampersand often denotes logical conjunction period |
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(3)
(mathematical context)
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verbose semantics |
Upper
A Ampersand Upper
B |
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§130. Asterisk, Dagger, Double Dagger, Number
Sign, Paragraph Mark, Section Mark, Star: The asterisk, dagger, double
dagger, number sign, paragraph mark, section mark, and star must be represented
by the symbols provided for them in this Code; the English Braille symbols must
be avoided even when the corresponding signs are used for purposes of
reference.
(1)
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verbose semantics |
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(2)
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verbose semantics |
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(3)
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verbose semantics |
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(4)
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verbose semantics |
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(5)
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verbose semantics |
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(6)
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verbose semantics |
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(7)
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verbose semantics |
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(8)
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verbose semantics |
Upper
A section-mark Upper
B |
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(9)
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verbose semantics |
Upper
A figure-star Upper
B |
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§131. Fraction Lines: For a complete
discussion of the rules governing fractions see Rule XII.
§132. Intersection, Union: When the
intersection sign or the union sign is modified by a superscribed bar, a
subscribed bar, or both, the combination is not longer a sign of operation but
a sign of comparison compounded vertically (see §147).
These signs
are frequently modified below, and are consequently printed wide enough to
accommodate the modifier. The variable width of these signs must be ignored in
the transcription. Superscripts or subscripts which are sometimes attached to
these signs must be treated in the usual manner for handling superscripts and
subscripts.
(1)
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verbose semantics |
Upper
A Intersection Upper
B |
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(2)
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verbose semantics |
Intersection Underscript
alpha Element-of Upper
A EndScripts
x Subscript
alpha |
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(3)
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verbose semantics |
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§133. Logical Product, Logical Sum: When
the signs for logical product or logical sum are modified by a
superscribed bar, a subscribed bar, or both, the combination is no longer a
sign of operation but a sign of comparison compounded vertically (see
§147).
(1)
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verbose semantics |
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(2)
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verbose semantics |
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§134. Minus Followed by Plus, Plus Followed
by Minus, Minus or Plus, Plus or Minus: When the signs for plus and minus are combined either vertically or horizontally, the
combination must be regarded as a single sign of operation. Its components must
not be divided between braille lines in the transcription.
(1)
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verbose semantics |
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(2)
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verbose semantics |
negative 3 plus negative 5 |
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(3)
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verbose semantics |
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(4)
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verbose semantics |
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§135. Multiplication: The two common
multiplication signs, cross and dot, must not be used interchangeably in the transcription. The
cross is sometimes modified below.
(1)
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verbose semantics |
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(2)
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verbose semantics |
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(3)
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verbose semantics |
times Underscript
alpha Element-of Upper
A EndScripts
Upper
A Subscript
alpha |
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§136. Slash: The slash must be
represented by the symbol provided for it in this Code. The English Braille
symbol must not be used.
(1)
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verbose semantics |
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(2)

,! rise_/run ratio is #3_4
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verbose semantics |
The rise slash run ratio is 3 period |
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(3)

#1 watt .k #1 joule_/sec4
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verbose semantics |
1 watt equals 1 joule slash seconds |
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(4)
(abbreviation meaning "care of")
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verbose semantics |
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(5)
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verbose semantics |
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(6)
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verbose semantics |
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(7)
(a date)
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verbose semantics |
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§137. Tilde: This sign of operation is
used predominantly in logic with the meaning of not.
(1)
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verbose semantics |
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(2)
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verbose semantics |
tilde p Logical-or tilde q Logical-or tilde r |
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(3)
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verbose semantics |
tilde tilde Upper
T Logical-or Upper
R |
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§138. Spacing with Symbols of Operation:
a. A
space must be left on either side of an operation symbol under any of the
circumstances listed below.
i. Between
a comparison symbol and an operation symbol.
(1)
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verbose semantics |
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ii. After a
function name or its abbreviation and before a symbol of operation.
(1)
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verbose semantics |
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iii. Between an
ellipsis or dash and a symbol of operation.
(1)
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verbose semantics |
1 plus 2 plus ellipsis plus n |
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(2)
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verbose semantics |
10 minus large-dash equals 8 |
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iv. Between an
abbreviation and a symbol of operation other than the fraction line or slash.
(1)
(in ink print, there is a space on both sides of the plus
sign)
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verbose semantics |
1 yards plus 2 yards equals 3 yards |
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v. Where required
according to Rule XXII.
(1)
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verbose semantics |
vertical-line vertical-line vertical-line vertical-line plus vertical-line vertical-line vertical-line vertical-line |
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b. A space must
not be left on either side of a symbol of operation in any other situation.
(1)
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verbose semantics |
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(2)
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verbose semantics |
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(3)
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verbose semantics |
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(4)
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verbose semantics |
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(5)
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verbose semantics |
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(6)
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verbose semantics |
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(7)
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verbose semantics |
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(8)
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verbose semantics |
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(9)
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verbose semantics |
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(10)

quotient@*divisor+remainder
.k dividend
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verbose semantics |
quotient times divisor plus remainder equals dividend |
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(11)

#3@*seven^2"+4@*seven^1"+5@*seven^0 .k #345;seven
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verbose semantics |
3 times seven squared plus 4 times seven Superscript
1 Baseline
plus 5 times seven Superscript
0 Baseline
equals 345 Subscript
seven |
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(12)
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verbose semantics |
left-parenthesis 2 n plus 3 right-parenthesis vertical-line 3 |
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(13)

#3 ft^2"+3 ft^2 .k #6 ft^2
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verbose semantics |
3 feet squared plus 3 feet squared equals 6 feet squared |
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