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Functional programming language for arrays
other programming languages. A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University.
APL_(programming_language)
Mathematical notation
mathematics, the Iverson bracket, named after Kenneth E. Iverson, is a notation that generalises the Kronecker delta, which is the Iverson bracket of the
Iverson_bracket
Topics referred to by the same term
Iverson notation can refer to: APL (programming language) Iverson bracket, in mathematics This disambiguation page lists articles associated with the
Iverson_notation
Canadian computer scientist (1920–2004)
Numbers, MIT Press, 1999, page 141. It was in this period that Iverson developed notation for describing and analyzing various topics in data processing
Kenneth_E._Iverson
Topics referred to by the same term
Iverson may refer to: Iverson Award, an ACM honour for APL contributions Iverson bracket, a mathematical notation Iverson Notation, the syntactic basis
Iverson
Origin and evolution of the symbols used to write equations and formulas
differential equations. In 1962, Kenneth E. Iverson developed an integral part notation, which became known as Iverson notation, that developed into APL. In the
History of mathematical notation
History_of_mathematical_notation
Nearest integers from a number
corresponding notations ⌊x⌋ and ⌈x⌉. (Iverson used square brackets for a different purpose, the Iverson bracket notation.) Both notations are now used
Floor_and_ceiling_functions
American computer scientist and mathematician
early host to IVSYS (for Iverson system), a predecessor of APL. In 1968, he became a colleague of Ken Iverson, used Iverson notation before APL was named
Eugene_McDonnell
Mathematical function characterizing set membership
(x)=0} otherwise. Other common notations are 𝟙A and χ A . {\displaystyle \chi _{A}.} The indicator function of A is the Iverson bracket of the property of
Indicator_function
Computer scientist and early Burning Man contributor
corresponded with APL's inventor, Ken Iverson, to correct the formal description of the IBM System/360 which used Iverson's notation. He received his M.S. from Stanford
Lawrence_M._Breed
Addition of several numbers or other values
\log(n)^{c}\cdot b^{n})} for non-negative real b > 1, c, d Capital-pi notation Einstein notation Iverson bracket Iterated binary operation Kahan summation algorithm
Summation
quantum cryptography pioneer Lawrence M. Breed – implementation of Iverson Notation (APL), co-developed APL\360, Scientific Time Sharing Corporation cofounder
List_of_computer_scientists
video games Paradroid and Uridium Larry Breed – implementation of Iverson Notation (APL), co-developed APL\360, Scientific Time Sharing Corporation cofounder
List_of_programmers
completes the proof of the theorem" to signal the end of a proof. Kenneth E. Iverson (1962), A Programming Language, Wiley, retrieved 20 April 2016 RapidTables:
Table of mathematical symbols by introduction date
Table_of_mathematical_symbols_by_introduction_date
Topics referred to by the same term
notation Binomial or multinomial coefficient Commutator, an indicator to which a binary operation fails to be commutative Iverson bracket, notation Lie
Math_symbol_brackets
after the decimal mark. This notation has also been used for other variants of floor and ceiling functions. 4. Iverson bracket: if P is a predicate,
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Marked objects for finding random numbers
(Discussion of dice that are fair "by symmetry" and "by continuity".) Iverson, G. R.; Longcour, W. H.; et al.; Bias and Runs in Dice Throwing and Recording:
Dice
Punctuation mark
variety of notations, including standard notations for commutators, the floor function, the Lie bracket, equivalence classes, the Iverson bracket, and
Bracket
Writing format
systematic and widespread use of medial capitals for technical purposes was the notation for chemical formulas invented by the Swedish chemist Jacob Berzelius in
Camel_case
Applying operations to whole sets of values simultaneously
Bibcode:2011CSE....13b..22V. doi:10.1109/mcse.2011.37. S2CID 16907816. Iverson, K. E. (1980). "Notation as a Tool of Thought". Communications of the ACM. 23 (8): 444–465
Array_programming
Brackets as used in mathematical notation
Binomial coefficient Bracket polynomial Bra-ket notation Delimiter Dyck language Frölicher–Nijenhuis bracket Iverson bracket Nijenhuis–Richardson bracket, also
Bracket_(mathematics)
American engineer (1932 - 2015)
Iverson's notation to describe the IBM 7090 computer. In early 1963, Falkoff, later joined by Iverson and Sussenguth, proceeded to use the notation to
Edward_H._Sussenguth
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
geometric series. Using the Iverson bracket: δ i j = [ i = j ] . {\displaystyle \delta _{ij}=[i=j].} Often, a single-argument notation δ i {\displaystyle \delta
Kronecker_delta
Indicator function of positive numbers
H(x):={\begin{cases}1,&x\geq 0\\0,&x<0\end{cases}}} Using the Iverson bracket notation: H ( x ) := [ x ≥ 0 ] {\displaystyle H(x):=[x\geq 0]} An indicator
Heaviside_step_function
Canadian computer programmer (1953–2021)
He codeveloped the programming language J with APL creator Kenneth E. Iverson. Hui was born in Hong Kong in 1953. In 1966, he immigrated to Canada with
Roger_Hui
Textbook by Ronald Graham, Donald Knuth, and Oren Patashnik
The book popularized some mathematical notation: the Iverson bracket, floor and ceiling functions, and notation for rising and falling factorials. Donald
Concrete_Mathematics
Programming language
of kdb+ and a new merged version of K and ksql. "KX Systems". Iverson, Kenneth. "Notation as a Tool of Thought". Archived from the original on 2013-09-20
K_(programming_language)
Design pattern in functional programming to build generic types
is a Database". ACM Queue. 10 (3): 20–33. doi:10.1145/2168796.2169076. Iverson, Kenneth (September 1987). "A dictionary of APL". APL Quote Quad. 18 (1):
Monad (functional programming)
Monad_(functional_programming)
Graphic representation of a molecular structure
1007/s10698-007-9033-2. ISSN 1386-4238. S2CID 93952251. Brown, William Henry; Brent L. Iverson; Eric V. Anslyn; Christopher S. Foote (2018). Organic chemistry (Eighth ed
Structural_formula
Symbol in mathematical logic
Inhaltsstrich, content stroke [—], came to be called the assertion sign." Frege's notation for a judgement of some content A ⊢ A {\displaystyle \vdash A} can then
Turnstile_(symbol)
Numerical symbol
Organisation. 2000. p. 15. ISO/FDIS 8601:2000(E). Retrieved 8 January 2019. Iverson, Cheryl; et al. (2007). AMA Manual of Style (10th ed.). Oxford, UK: Oxford
Decimal_separator
American computer scientist
language APL. In 1962, Kenneth E. Iverson published his book A Programming Language, describing a mathematical notation for describing array operations
Philip_S._Abrams
American annual computer science prize
Award Laureate". amturing.acm.org. Retrieved October 18, 2025. Iverson, K. E. (1980). "Notation as a tool of thought". Communications of the ACM. 23 (8): 444–465
Turing_Award
Numbers parameterizing ways to partition a set
{\displaystyle \lbrace \textstyle {n \atop k}\rbrace } or with other notations, count the number of ways to partition a set of n {\displaystyle n} labelled
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Programming paradigm based on applying and composing functions
In the early 1990s, Iverson and Roger Hui created J. In the mid-1990s, Arthur Whitney, who had previously worked with Iverson, created K, which is used
Functional_programming
programming languages were highly specialized, relying on mathematical notation and similarly obscure syntax. Throughout the 20th century, research in
History of programming languages
History_of_programming_languages
Alternate way to define a function in APL
1980). "Notation as a Tool of Thought". Communications of the ACM. 23 (8): 444–465. doi:10.1145/358896.358899. Retrieved 8 April 2016. Iverson, Kenneth
Direct_function
American computer scientist
language, and was the inventor of the Backus–Naur form (BNF), a widely used notation to define syntaxes of formal languages. He also contributed to the design
John_Backus
Relation between pairs of arithmetic functions
{n}{d}}\right)^{\mu (d)}.} The first generalization can be proved as follows. We use Iverson's convention that [condition] is the indicator function of the condition
Möbius_inversion_formula
Set of rules defining correctly structured programs
symbols, not words. These symbols were originally devised as a mathematical notation to describe algorithms. APL programmers often assign informal names when
APL_syntax_and_symbols
Conversion of an optically active chemical compound into an inactive form
non-superposable when rotated in 3-dimensional space, are said to be enantiomers. The notation is not to be confused with D and L naming of molecules which refers to
Racemization
Function returning minus 1, zero or plus 1
{\text{for }}x\neq 0\,.} The signum can also be written using the Iverson bracket notation: sgn x = [ x > 0 ] − [ x < 0 ] . {\displaystyle \operatorname
Sign_function
Concept in computer science
programming language based on non-deterministic conditionals Guarded suspension Iverson bracket Logical conditional Switch statement Beck, Kent (1997). "Guard
Guard_(computer_science)
Piecewise function that clamps its input to be non-negative
R(x):={\begin{cases}x,&x\geq 0;\\0,&x<0\end{cases}}} Using the Iverson bracket notation: R ( x ) := x ⋅ [ x ≥ 0 ] {\displaystyle R(x):=x\cdot [x\geq 0]}
Ramp_function
Origami of a crane (bird)
MEANING OF THE ORIGAMI CRANE (n.d.): n. pag. Web. 16 Feb. 2017. Patsy Wang-Iverson, Robert J. Lang, Mark Yim Origami 5: Fifth International Meeting of Origami
Orizuru
Logical formalism using combinators instead of variables
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell
Combinatory_logic
Setting or re-setting the value associated with a variable name
used notation for this operation is x = expr (originally Superplan 1949–51, popularized by Fortran 1957 and C). The second most commonly used notation is
Assignment_(computer_science)
Elements in exactly one of two sets
\chi _{(A\,\Delta \,B)}=\chi _{A}\oplus \chi _{B}} or using the Iverson bracket notation [ x ∈ A Δ B ] = [ x ∈ A ] ⊕ [ x ∈ B ] {\displaystyle [x\in A\,\Delta
Symmetric_difference
Discrete probability distribution
complex but facilitates mathematical manipulations is as follows, using the Iverson bracket: f ( x ∣ p ) = ∏ i = 1 k p i [ x = i ] , {\displaystyle f(x\mid
Categorical_distribution
1016/S0066-4138(61)80008-6. ISSN 0066-4138. Smillie, Keith. "Kenneth E. Iverson – A.M. Turing Award Winner". ACM. "Ken Thompson interviewed by Brian Kernighan
Timeline of programming languages
Timeline_of_programming_languages
interest in origami dates to the design in 1954 by Akira Yoshizawa of a notation to indicate how to fold origami models. The Yoshizawa-Randlett system is
History_of_origami
British computer scientist (1948-2019)
1980). "Notation as a Tool of Thought". Communications of the ACM. 23 (8): 444–465. doi:10.1145/358896.358899. Retrieved 8 April 2016. Iverson, Kenneth
John_M._Scholes
Hypothesis of language influencing thought
Rewriting the World, Paul J. J. Payack, (C) 2007, p. 194. Iverson, Kenneth E. (August 1980). "Notation as a tool of thought". Communications of the ACM. 23
Linguistic_relativity
Statistic measuring inter-rater agreement for categorical items
, j := [ i ≠ j ] {\displaystyle W_{i,j}:=[i\neq j]} using the Iverson bracket notation), this produces the same value as the unweighted kappa calculation
Cohen's_kappa
Rational number sequence
The expression [n even] has the value 1 if n is even and 0 otherwise (Iverson bracket). These identities show that the quotient of Bernoulli and Euler
Bernoulli_number
Punctuation mark used to join words
those that end -ly, are less likely to need hyphens [example elided]. Iverson, Cheryl (2007). "8.3.1". AMA Manual of Style (10th ed.). Oxford, Oxfordshire:
Hyphen
Musical work by György Ligeti
Sounds, p. 130, n. 33. Boydell & Brewer. ISBN 9781843835509. Jennifer Joy Iverson, " Historical Memory and György Ligeti's Sound-Mass Music 1958–1968", PhD
Artikulation_(Ligeti)
Statistical regression where the dependent variable can take only two values
normal distribution within the given ranges. The notation [ z i < 0 ] {\displaystyle [z_{i}<0]} is the Iverson bracket, sometimes written I ( z i < 0 ) {\displaystyle
Probit_model
American computer engineer (1921–2010)
since 1955 for over forty years before retiring. He collaborated with Ken Iverson from 1960 to 1980 on the design, development, and use of the APL programming
Adin_Falkoff
}}x{\text{ counted by multiplicities}}} See also: Prime omega function. The Iverson bracket is [ P ] = { 1 if P is true, 0 if P is false. {\displaystyle
Feller–Tornier_constant
with Hindu Numerals. 1970, 1989 Allen, Frances E. Developed bit vector notation and program control-flow graphs; first female IBM Fellow (1989); first
List of pioneers in computer science
List_of_pioneers_in_computer_science
Software that translates code from one programming language to another
until the 1970s, it presented concepts later seen in APL designed by Ken Iverson in the late 1950s. APL is a language for mathematical computations. Between
Compiler
Random process of binary (boolean) random variables
with x i = [ ω i = H ] {\displaystyle x_{i}=[\omega _{i}=H]} in Iverson bracket notation, meaning either 1 {\displaystyle 1} if ω i = H {\displaystyle \omega
Bernoulli_process
Polynomial sequence
\right\rangle ,} with initial condition for n = 0, expressed in Iverson bracket notation: ⟨ ⟨ 0 k ⟩ ⟩ = [ k = 0 ] . {\displaystyle \left\langle \!\!\left\langle
Eulerian_number
write reconstructed Proto-Indo-European words (for an explanation of the notation, see Proto-Indo-European phonology). Without proper rendering support,
Glossary of sound laws in the Indo-European languages
Glossary_of_sound_laws_in_the_Indo-European_languages
Problem in statistical estimation
probability 1/n for m ≤ n, and zero probability for m > n. Using Iverson bracket notation this is written ( M = m ∣ N = n , K = 1 ) = ( m ∣ n ) = [ m ≤ n
German_tank_problem
Count of permutations by cycles
The notations used on this page for Stirling numbers are not universal, and may conflict with notations in other sources; the square bracket notation [
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Type of speech sound
(1997) Both cited in Hamann (2003, pp. 25–26) Esling (2010), p. 699. "Ahn & Iverson (2006)" (PDF), archived from the original (PDF) on 2011-07-20, retrieved
Approximant
American jazz musician
studio talking to himself... Lowell made Sun Ra look normal." Pianist Ethan Iverson described Davidson as having "an approach somewhere between the fury of
Lowell_Davidson
Number of prime factors of a natural number
x}\omega (n)[n{\text{ odd}}],} where [ ⋅ ] {\displaystyle [\cdot ]} denotes Iverson bracket. Then we have that S odd ( x ) = x 2 log log x + ( 2 B 1 −
Prime_omega_function
Systematic classification of 12 related enumerative problems concerning two finite sets
k ! {\textstyle {\binom {n}{k}}={\frac {n^{\underline {k}}}{k!}}} the Iverson bracket [ ] encoding a truth value as 0 or 1 the number p k ( n ) {\textstyle
Twelvefold_way
Sound system of the Korean language
University of New York Press. p. 66. ISBN 978-0-7914-4831-1. Ahn, Sang-Cheol; Iverson, Gregory K. (2005). "Structured imbalances in the emergence of the Korean
Korean_phonology
Family of probability distributions related to the normal distribution
is false, the Iverson bracket is zero. There are many variant notations, e.g. wavey brackets: ⧙a=b⧘ is equivalent to the [a=b] notation used above. The
Exponential_family
Hungarian composer (1923–2006)
1999, 38. Steinitz 2003, 60. Steinitz 2003, 63–64. Steinitz 2003, 75. Iverson 2009, 92. Jones n.d. Istvan Szigeti (29 July 1983). "A Budapest Interview
György_Ligeti
of Theological Studies, vol. 27, nr. 108 (July 1926) page 107; Kelly R. Iverson, A Further Word on Final Γάρ (Mark 16:8), Catholic Bible Quarterly, vol
List of New Testament verses not included in modern English translations
List_of_New_Testament_verses_not_included_in_modern_English_translations
Computer programming operation
procedure call) to be omitted when used as an actual parameter. Kenneth Iverson's APL (1957) had very flexible multi-dimensional array slicing, which contributed
Array_slicing
Statistical measure of the magnitude of a phenomenon
{\displaystyle x_{j}} , respectively, and [ ⋅ ] {\displaystyle [\cdot ]} is the Iverson bracket, which is 1 when the contents are true and 0 when false. d {\displaystyle
Effect_size
Cengage Learning. p. 157. ISBN 9780547168043. William Henry Brown; Brent L. Iverson (2009). Organic chemistry (5, illustrated ed.). Cengage Learning. p. 621
List_of_chemistry_mnemonics
708–715. doi:10.3384/ecp09430044. ISBN 9789173935135. Flueckiger, Scott M.; Iverson, Brian D.; Garimella, Suresh V.; Pacheco, James E. (2014-01-01). "System-level
System-level_simulation
Range of mainframe computers in the 1960s and 70s
languages, including the object-oriented Simula (a superset of ALGOL), and Iverson, the designer of APL declared that the Burroughs implementation of APL
Burroughs_Large_Systems
English cricketer
place at the same time. Qualification: 10 wickets, career completed. The notation 6/59 means that the bowler took six wickets at the cost of 59 runs scored
Charles_Marriott
Process in which a first language is being acquired
PMC 3834520. PMID 24312022. Kuhl P, Stevens E, Hayashi A, Deguchi T, Kiritani S, Iverson P (February 2006). "Infants show a facilitation effect for native language
Language_acquisition
Basketball player selection
Albuquerque (Sr.) Jim Garza, Detroit Institute of Technology (Sr.) Willie Iverson, Central Michigan University (Sr.) Terry Porter, St. Cloud State University
1968_ABA_draft
Chapter of the New Testament
2022, accessed 26 March 2023 Julie M. Smith, The Ending of Mark’s Gospel Iverson, Kelly (April 2001). Irony in the End: A Textual and Literary Analysis
Mark_16
Beechcraft; member of the National Academy of Engineering (1977) F. Kenneth Iverson (1946, aeronautical engineering) – president of Nucor Steel (1967–1998);
List of Cornell University alumni
List_of_Cornell_University_alumni
Mathematical term
\right]_{\delta },} where [ ⋅ ] δ {\displaystyle [\cdot ]_{\delta }} denotes Iverson's convention, then we have the coefficients for the t t h {\displaystyle
Lambert_series
Type of statistical inference
0005. JSTOR 91337. Wagenmakers, Eric-Jan; Lee, Michael; Lodewyckx, Tom; Iverson, Geoffrey J. (2008), "Bayesian Versus Frequentist Inference", in Hoijtink
Frequentist_inference
Andrew Jackson controversy
Watson (2012), pp. 68–69. Feller (2010), p. 313. Watson (2012), p. 137. Iverson, Justin (2019). "Fugitives on the Front: Maroons in the Gulf Coast Borderlands
Rhea_letter
American music theorist-analyst and composer
Review. 40 (2–3): 327. doi:10.1080/07494467.2021.1989224. S2CID 245730696. Iverson, Ethan (2021). "Back to Babbitt (with Erik Carlson)". Do the M@th. Maggart
Joshua_Banks_Mailman
Handbook of Logic in Computer Science Jean-Raymond Abrial, father of the Z notation and the B-Method, targeted at the clear specification and refinement of
List of programming language researchers
List_of_programming_language_researchers
American painter (1891–1978)
paintings, often share with them the quality of the Freudian uncanny that Iverson found in Edward Hopper's work, a quality to which the hazy luminosity contributes
Edwin_Dickinson
Aquifer contamination by medical drugs
1155/2017/3039817. Brown, William Henry (2018). Organic chemistry. Brent L. Iverson, Eric V. Anslyn, Christopher S. Foote (Eighth ed.). Australia. ISBN 978-1-305-58035-0
Groundwater contamination by pharmaceuticals
Groundwater_contamination_by_pharmaceuticals
IVERSON NOTATION
IVERSON NOTATION
Surname or Lastname
English (London)
English (London) : patronymic from the personal name Piers (see Pierce).North German : patronymic from the personal name Pier, a variant of Peer, reduced form of Peter.Born in Yorkshire, England, Abraham Pierson (1609–78) was the first pastor of the settlements at Southampton, Long Island, NY; Branford, CT, and Newark, NJ. He left his library of more than 400 books, one of the most extensive in the colonies, to his son Abraham, who was one of the first trustees of Yale College.
Surname or Lastname
English and Scottish
English and Scottish : patronymic from the Old Norse personal name Ãvarr, a compound of either Ãv ‘yew tree’, ‘bow’ or Ing (the name of a god) + ar ‘warrior’ or ‘spear’.Swedish equivalent of Iversen 1.Respelling of Danish, Norwegian, and North German Iversen.
Surname or Lastname
English
English : variant of Emerson.
Male
English
English surname transferred to forename use, from a Norman French baronial name VERNON means "place of alder trees."
Surname or Lastname
English
English : probably a variant spelling of Gibbeson, a patronymic from Gibb.
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from Vernon in Eure, France, named from the Gaulish element ver(n) ‘alder’ + the Gallo-Roman locative suffix -o (genitive -Ånis).French : habitational name from the same place as in 1 or from any of numerous other places in France with the same name and etymology.
Surname or Lastname
English
English : patronymic from Lever 3.
Surname or Lastname
English
English : patronymic from the personal name Ever (see Evers 2).
Surname or Lastname
English
English : variant of Steverson.
Surname or Lastname
English
English : patronymic from the personal name Simon.
Surname or Lastname
English
English : habitational name from any of the numerous places so called. Most are named from Old English uferra ‘upper’ + tÅ«n ‘enclosure’, ‘settlement’; others have Old English Åfer ‘riverbank’ or ofer ‘slope’ as the first element.
Surname or Lastname
English
English : patronymic from Mayer or Myer.
Boy/Male
English American German
Brave; powerful.
Surname or Lastname
French
French : habitational name from a place so named, for example in Dordogne, Gironde, and Marne.English : variant of Verdun.A Verdon, also written Verdun, from the Aunis region of France was documented in Quebec City in 1663.
Male
English
English surname transferred to forename use, EMERSON means "son of Emery."
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : patronymic from the Old French personal name Ive.
Surname or Lastname
Danish and Norwegian
Danish and Norwegian : patronymic from the personal name Ivar, from Old Norse Ãvarr, a compound of either Ãv ‘yew tree’, ‘bow’ or Ing (the name of a god) + ar ‘warrior’ or ‘spear’.North German (Frisian) : patronymic from a Germanic personal name composed of the elements Ä«wa ‘yew (tree)’ + hard ‘strong’, ‘firm’.English : variant spelling of Iverson.
Surname or Lastname
English
English : habitational name from any of various places, in Bedfordshire, Merseyside, and Nottinghamshire, so named from Old English eofor ‘wild boar’ + tūn ‘settlement’.Described as being from Kent, England, Walter Everendon (d. 1725) was a colonial gunpowder manufacturer who ran a mill in Neponset in the township of Milton, across the river from Dorchester, MA. The first person to make gunpowder in America, Everendon eventually took majority interest in the mill and sold out to his son. The family, which also spelled their name Everden and Everton, continued to manufacture powder until after the Revolution.
Surname or Lastname
English
English : patronymic from the personal name Emery.The poet and essayist Ralph Waldo Emerson (1803–82) was born in Boston of a line on his father’s side that can be traced back through preachers to the first colonial generation. The name Emerson was brought over from England independently by various other people, including a Thomas Emerson who settled at Ipswich, MA, in about 1636.
Boy/Male
English
Boar town. Hardy; brave.
IVERSON NOTATION
IVERSON NOTATION
Girl/Female
American, British, English
Hazelnut; Variant of Medieval Given Names Avis and Aveline
Girl/Female
Muslim
Captivating, Alluring, Intelligent
Girl/Female
Arabic
Perfect.
Boy/Male
Shakespearean
All's Well That Ends Well.' An old lord.
Male
Arthurian
, (lake), a king; the father of Erec.
Boy/Male
Hindu
Another name of Lord Krishna, Sweet like Honey
Boy/Male
Hindu
Lord Shivas name
Boy/Male
Hindu
Of the form of the entire universe
Girl/Female
Muslim
Well born
Boy/Male
Biblical
Father of a target; father of coldness.
IVERSON NOTATION
IVERSON NOTATION
IVERSON NOTATION
IVERSON NOTATION
IVERSON NOTATION
n.
Said of a subject, or phrase, when the intervals of which it consists are repeated in the contrary direction, rising instead of falling, or vice versa.
n.
Said of a chord, when one of its notes, other than its root, is made the bass.
n.
A translation; that which is rendered from another language; as, the Common, or Authorized, Version of the Scriptures (see under Authorized); the Septuagint Version of the Old Testament.
n.
The act of translating, or rendering, from one language into another language.
v. t.
To represent as a person; to personify; to impersonate.
n.
Said of intervals, when the lower tone is placed an octave higher, so that fifths become fourths, thirds sixths, etc.
n.
A change of form, direction, or the like; transformation; conversion; turning.
n.
A human being spoken of indefinitely; one; a man; as, any person present.
n.
A condition of the uterus in which its axis is deflected from its normal position without being bent upon itself. See Anteversion, and Retroversion.
n.
An account or description from a particular point of view, especially as contrasted with another account; as, he gave another version of the affair.
n.
The act of turning aside from any course, occupation, or object; as, the diversion of a stream from its channel; diversion of the mind from business.
n.
A change of the usual order of words or phrases; as, "of all vices, impurity is one of the most detestable," instead of, "impurity is one of the most detestable of all vices."
n.
A change in the order of the terms of a proportion, so that the second takes the place of the first, and the fourth of the third.
n.
Said of double counterpoint, when an upper and a lower part change places.
n.
The bodily form of a human being; body; outward appearance; as, of comely person.
n.
A method of reasoning in which the orator shows that arguments advanced by his adversary in opposition to him are really favorable to his cause.
n.
The folding back of strata upon themselves, as by upheaval, in such a manner that the order of succession appears to be reversed.
n.
The state of being turned back or outward; as, eversion of eyelids; ectropium.
n.
A peculiar method of transformation, in which a figure is replaced by its inverse figure. Propositions that are true for the original figure thus furnish new propositions that are true in the inverse figure. See Inverse figures, under Inverse.
n.
The act or process by which cane sugar (sucrose), under the action of heat and acids or ferments (as diastase), is broken or split up into grape sugar (dextrose), and fruit sugar (levulose); also, less properly, the process by which starch is converted into grape sugar (dextrose).