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45-450: (Redirected from Rockrose ) Rock rose , rock-rose , and rockrose are common names of various plants, including: Cistaceae Cistus Halimium Helianthemum Pavonia lasiopetala Phemeranthus Portulaca grandiflora [REDACTED] Index of plants with the same common name This page is an index of articles on plant species (or higher taxonomic groups) with

90-410: A {\displaystyle a} (although there is per definitionem never an "ambiguous function"), and the original "definition" is pointless. Despite these subtle logical problems, it is quite common to use the term definition (without apostrophes) for "definitions" of this kind, for three reasons: Questions regarding the well-definedness of a function often arise when the defining equation of

135-578: A ) {\displaystyle f(a)} is "ambiguous" for a ∈ A 0 ∩ A 1 {\displaystyle a\in A_{0}\cap A_{1}} . For example, if A 0 := { 2 } {\displaystyle A_{0}:=\{2\}} and A 1 := { 2 } {\displaystyle A_{1}:=\{2\}} , then f ( 2 ) {\displaystyle f(2)} would have to be both 0 and 1, which makes it ambiguous. As

180-453: A ) {\displaystyle f(a)} would be well defined and equal to mod ⁡ ( a , 2 ) {\displaystyle \operatorname {mod} (a,2)} . However, if A 0 ∩ A 1 ≠ ∅ {\displaystyle A_{0}\cap A_{1}\neq \emptyset } , then f {\displaystyle f} would not be well defined because f (

225-867: A ) = 0 {\displaystyle f(a)=0} if a ∈ A 0 {\displaystyle a\in A_{0}} and f ( a ) = 1 {\displaystyle f(a)=1} if a ∈ A 1 {\displaystyle a\in A_{1}} . Then f {\displaystyle f} is well defined if A 0 ∩ A 1 = ∅ {\displaystyle A_{0}\cap A_{1}=\emptyset \!} . For example, if A 0 := { 2 , 4 } {\displaystyle A_{0}:=\{2,4\}} and A 1 := { 3 , 5 } {\displaystyle A_{1}:=\{3,5\}} , then f (

270-438: A , 1 ) ∈ f {\displaystyle (a,1)\in f} , which makes the binary relation f {\displaystyle f} not functional (as defined in Binary relation#Special types of binary relations ) and thus not well defined as a function. Colloquially, the "function" f {\displaystyle f} is also called ambiguous at point

315-400: A ] {\displaystyle [a]} as a + k n {\displaystyle a+kn} , where k {\displaystyle k} is an integer. Therefore, similar holds for any representative of [ b ] {\displaystyle [b]} , thereby making [ a + b ] {\displaystyle [a+b]} the same, irrespective of

360-639: A function refers not only to the arguments themselves, but also to elements of the arguments, serving as representatives . This is sometimes unavoidable when the arguments are cosets and when the equation refers to coset representatives. The result of a function application must then not depend on the choice of representative. For example, consider the following function: where n ∈ Z , m ∈ { 4 , 8 } {\displaystyle n\in \mathbb {Z} ,m\in \{4,8\}} and Z / m Z {\displaystyle \mathbb {Z} /m\mathbb {Z} } are

405-468: A function – is well defined. On the other hand, if A 0 ∩ A 1 ≠ ∅ {\displaystyle A_{0}\cap A_{1}\neq \emptyset } , then for an a ∈ A 0 ∩ A 1 {\displaystyle a\in A_{0}\cap A_{1}} , we would have that ( a , 0 ) ∈ f {\displaystyle (a,0)\in f} and (

450-485: A particularly common name is used varies; some common names have a very local application, while others are virtually universal within a particular language. Some such names even apply across ranges of languages; the word for cat , for instance, is easily recognizable in most Germanic and many Romance languages . Many vernacular names, however, are restricted to a single country and colloquial names to local districts. Some languages also have more than one common name for

495-399: A result, the latter f {\displaystyle f} is not well defined and thus not a function. In order to avoid the quotation marks around "define" in the previous simple example, the "definition" of f {\displaystyle f} could be broken down into two logical steps: While the definition in step 1 is formulated with the freedom of any definition and

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540-433: A single chemical, such as copper sulfate , which may refer to either copper(I) sulfate or copper(II) sulfate. Sometimes common names are created by authorities on one particular subject, in an attempt to make it possible for members of the general public (including such interested parties as fishermen, farmers, etc.) to be able to refer to one particular species of organism without needing to be able to memorise or pronounce

585-486: Is a global system that attempts to denote particular organisms or taxa uniquely and definitively , on the assumption that such organisms or taxa are well-defined and generally also have well-defined interrelationships; accordingly the ICZN has formal rules for biological nomenclature and convenes periodic international meetings to further that purpose. The form of scientific names for organisms, called binomial nomenclature ,

630-400: Is certainly effective (without the need to classify it as "well defined"), the assertion in step 2 has to be proven. That is, f {\displaystyle f} is a function if and only if A 0 ∩ A 1 = ∅ {\displaystyle A_{0}\cap A_{1}=\emptyset } , in which case f {\displaystyle f} – as

675-438: Is considered "well-defined". On the other hand, Division is non-associative, and in the case of a / b / c {\displaystyle a/b/c} , parenthesization conventions are not well established; therefore, this expression is often considered ill-defined. Unlike with functions, notational ambiguities can be overcome by means of additional definitions (e.g., rules of precedence , associativity of

720-404: Is different from Wikidata All set index articles Common name In chemistry , IUPAC defines a common name as one that, although it unambiguously defines a chemical, does not follow the current systematic naming convention, such as acetone , systematically 2-propanone , while a vernacular name describes one used in a lab, trade or industry that does not unambiguously describe

765-461: Is in these remarks from a book on marine fish: In scientific binomial nomenclature, names commonly are derived from classical or modern Latin or Greek or Latinised forms of vernacular words or coinages; such names generally are difficult for laymen to learn, remember, and pronounce and so, in such books as field guides, biologists commonly publish lists of coined common names. Many examples of such common names simply are attempts to translate

810-442: Is not well defined (and thus not a function). The term well-defined can also be used to indicate that a logical expression is unambiguous or uncontradictory. A function that is not well defined is not the same as a function that is undefined . For example, if f ( x ) = 1 x {\displaystyle f(x)={\frac {1}{x}}} , then even though f ( 0 ) {\displaystyle f(0)}

855-454: Is superficially similar to the noun-adjective form of vernacular names or common names which were used by non-modern cultures. A collective name such as owl was made more precise by the addition of an adjective such as screech . Linnaeus himself published a flora of his homeland Sweden, Flora Svecica (1745), and in this, he recorded the Swedish common names, region by region, as well as

900-650: Is the Cape dikkop (or "gewone dikkop", not to mention the presumably much older Zulu name "umBangaqhwa"); Burhinus vermiculatus is the "water dikkop". The thick joints in question are not even, in fact, the birds' knees, but the intertarsal joints —in lay terms the ankles. Furthermore, not all species in the genus have "thick knees", so the thickness of the "knees" of some species is not of clearly descriptive significance. The family Burhinidae has members that have various common names even in English, including " stone curlews ", so

945-569: Is the argument of f {\displaystyle f} . The function f {\displaystyle f} is well defined, because: As a counter example, the converse definition: does not lead to a well-defined function, since e.g. 1 ¯ 4 {\displaystyle {\overline {1}}_{4}} equals 5 ¯ 4 {\displaystyle {\overline {5}}_{4}} in Z / 4 Z {\displaystyle \mathbb {Z} /4\mathbb {Z} } , but

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990-463: Is the case with say, ginkgo , okapi , and ratel . Folk taxonomy , which is a classification of objects using common names, has no formal rules and need not be consistent or logical in its assignment of names, so that say, not all flies are called flies (for example Braulidae , the so-called "bee lice") and not every animal called a fly is indeed a fly (such as dragonflies and mayflies ). In contrast, scientific or biological nomenclature

1035-532: Is undefined, this does not mean that the function is not well defined; rather, 0 is not in the domain of f {\displaystyle f} . Let A 0 , A 1 {\displaystyle A_{0},A_{1}} be sets, let A = A 0 ∪ A 1 {\displaystyle A=A_{0}\cup A_{1}} and "define" f : A → { 0 , 1 } {\displaystyle f:A\rightarrow \{0,1\}} as f (

1080-526: The integers modulo m and n ¯ m {\displaystyle {\overline {n}}_{m}} denotes the congruence class of n mod m . N.B.: n ¯ 4 {\displaystyle {\overline {n}}_{4}} is a reference to the element n ∈ n ¯ 8 {\displaystyle n\in {\overline {n}}_{8}} , and n ¯ 8 {\displaystyle {\overline {n}}_{8}}

1125-570: The Hebrew Language publish from time to time short dictionaries of common name in Hebrew for species that occur in Israel or surrounding countries e.g. for Reptilia in 1938, Osteichthyes in 2012, and Odonata in 2015. Well-defined In mathematics , a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise,

1170-683: The SSAR switched to an online version with a searchable database. Standardized names for the amphibians and reptiles of Mexico in Spanish and English were first published in 1994, with a revised and updated list published in 2008. A set of guidelines for the creation of English names for birds was published in The Auk in 1978. It gave rise to Birds of the World: Recommended English Names and its Spanish and French companions. The Academy of

1215-524: The Secretariat for the AFNC. SSA is an accredited Standards Australia (Australia's peak non-government standards development organisation) Standards Development The Entomological Society of America maintains a database of official common names of insects, and proposals for new entries must be submitted and reviewed by a formal committee before being added to the listing. Efforts to standardize English names for

1260-501: The amphibians and reptiles of North America (north of Mexico) began in the mid-1950s. The dynamic nature of taxonomy necessitates periodical updates and changes in the nomenclature of both scientific and common names. The Society for the Study of Amphibians and Reptiles (SSAR) published an updated list in 1978, largely following the previous established examples, and subsequently published eight revised editions ending in 2017. More recently

1305-509: The author introduced into it so many new English names, that are to be found in no dictionary, and that do not preclude the necessity of learning with what Latin names they are synonymous. A tolerable idea may be given of the danger of too great a multiplicity of vulgar names, by imagining what geography would be, or, for instance, the Post-office administration, supposing every town had a totally different name in every language. Various bodies and

1350-493: The authors of many technical and semi-technical books do not simply adapt existing common names for various organisms; they try to coin (and put into common use) comprehensive, useful, authoritative, and standardised lists of new names. The purpose typically is: Other attempts to reconcile differences between widely separated regions, traditions, and languages, by arbitrarily imposing nomenclature, often reflect narrow perspectives and have unfortunate outcomes. For example, members of

1395-494: The choice of representative. For real numbers, the product a × b × c {\displaystyle a\times b\times c} is unambiguous because ( a × b ) × c = a × ( b × c ) {\displaystyle (a\times b)\times c=a\times (b\times c)} ; hence the notation is said to be well defined . This property, also known as associativity of multiplication, guarantees

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1440-408: The choice of the name "thick-knees" is not easy to defend but is a clear illustration of the hazards of the facile coinage of terminology. For collective nouns for various subjects, see a list of collective nouns (e.g. a flock of sheep, pack of wolves). Some organizations have created official lists of common names, or guidelines for creating common names, hoping to standardize

1485-528: The expression is said to be not well defined , ill defined or ambiguous . A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if f {\displaystyle f} takes real numbers as input, and if f ( 0.5 ) {\displaystyle f(0.5)} does not equal f ( 1 / 2 ) {\displaystyle f(1/2)} then f {\displaystyle f}

1530-646: The first would be mapped by g {\displaystyle g} to 1 ¯ 8 {\displaystyle {\overline {1}}_{8}} , while the second would be mapped to 5 ¯ 8 {\displaystyle {\overline {5}}_{8}} , and 1 ¯ 8 {\displaystyle {\overline {1}}_{8}} and 5 ¯ 8 {\displaystyle {\overline {5}}_{8}} are unequal in Z / 8 Z {\displaystyle \mathbb {Z} /8\mathbb {Z} } . In particular,

1575-517: The genus Burhinus occur in Australia, Southern Africa, Eurasia, and South America. A recent trend in field manuals and bird lists is to use the name " thick-knee " for members of the genus. This, in spite of the fact that the majority of the species occur in non-English-speaking regions and have various common names, not always English. For example, "Dikkop" is the centuries-old South African vernacular name for their two local species: Burhinus capensis

1620-706: The modern (now binding) International Code of Nomenclature for algae, fungi, and plants contains the following: Art. 68. Every friend of science ought to be opposed to the introduction into a modern language of names of plants that are not already there unless they are derived from a Latin botanical name that has undergone but a slight alteration. ... ought the fabrication of names termed vulgar names, totally different from Latin ones, to be proscribed. The public to whom they are addressed derives no advantage from them because they are novelties. Lindley's work, The Vegetable Kingdom, would have been better relished in England had not

1665-426: The operator). For example, in the programming language C , the operator - for subtraction is left-to-right-associative , which means that a-b-c is defined as (a-b)-c , and the operator = for assignment is right-to-left-associative , which means that a=b=c is defined as a=(b=c) . In the programming language APL there is only one rule: from right to left – but parentheses first. A solution to

1710-420: The result does not depend on the sequence of multiplications; therefore, a specification of the sequence can be omitted. The subtraction operation is non-associative; despite that, there is a convention that a − b − c {\displaystyle a-b-c} is shorthand for ( a − b ) − c {\displaystyle (a-b)-c} , thus it

1755-421: The same common name ( vernacular name). If an internal link led you here, you may wish to edit the linking article so that it links directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Rock_rose&oldid=1096295108 " Category : Set index articles on plant common names Hidden categories: Articles with short description Short description

1800-484: The same animal. For example, in Irish, there are many terms that are considered outdated but still well-known for their somewhat humorous and poetic descriptions of animals. w/ literal translations of the poetic terms Common names are used in the writings of both professionals and laymen . Lay people sometimes object to the use of scientific names over common names, but the use of scientific names can be defended, as it

1845-402: The scientific name into English or some other vernacular. Such translation may be confusing in itself, or confusingly inaccurate, for example, gratiosus does not mean "gracile" and gracilis does not mean "graceful". The practice of coining common names has long been discouraged; de Candolle's Laws of Botanical Nomenclature , 1868, the non-binding recommendations that form the basis of

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1890-555: The scientific name. Creating an "official" list of common names can also be an attempt to standardize the use of common names, which can sometimes vary a great deal between one part of a country and another, as well as between one country and another country, even where the same language is spoken in both places. A common name intrinsically plays a part in a classification of objects, typically an incomplete and informal classification, in which some names are degenerate examples in that they are unique and lack reference to any other name, as

1935-579: The scientific names. The Swedish common names were all binomials (e.g. plant no. 84 Råg-losta and plant no. 85 Ren-losta); the vernacular binomial system thus preceded his scientific binomial system. Linnaean authority William T. Stearn said: By the introduction of his binomial system of nomenclature, Linnaeus gave plants and animals an essentially Latin nomenclature like vernacular nomenclature in style but linked to published, and hence relatively stable and verifiable, scientific concepts and thus suitable for international use. The geographic range over which

1980-450: The term well-defined is used with respect to (binary) operations on cosets. In this case, one can view the operation as a function of two variables, and the property of being well-defined is the same as that for a function. For example, addition on the integers modulo some n can be defined naturally in terms of integer addition. The fact that this is well-defined follows from the fact that we can write any representative of [

2025-800: The use of common names. For example, the Australian Fish Names List or AFNS was compiled through a process involving work by taxonomic and seafood industry experts, drafted using the CAAB (Codes for Australian Aquatic Biota) taxon management system of the CSIRO , and including input through public and industry consultations by the Australian Fish Names Committee (AFNC). The AFNS has been an official Australian Standard since July 2007 and has existed in draft form (The Australian Fish Names List) since 2001. Seafood Services Australia (SSA) serve as

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