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For example, one might say that: "Given an arbitrary integer, multiplying it by two will result in an even number." Even further, the implication of the use of "arbitrary" is that generality will hold—even if an opponent were to choose the item in question. In which case, arbitrary can be regarded as synonymous to worst-case. [5]
An arbitrary trademark is usually a common word which is used in a meaningless context (e.g. "Apple" for computers). Such marks consist of words or images which have some dictionary meaning before being adopted as trademarks, but which are used in connection with products or services unrelated to that dictionary meaning.
This process can create arbitrarily long words: for example, the prefixes pseudo (false, spurious) and anti (against, opposed to) can be added as many times as desired. More familiarly, the addition of numerous "great"s to a relative, such as "great-great-great-great-grandparent", can produce words of arbitrary length.
See also List of Ship of Theseus examples. Sorites paradox (also known as the paradox of the heap): If one removes a single grain of sand from a heap, they still have a heap. If they keep removing single grains, the heap will disappear. Can a single grain of sand make the difference between heap and non-heap?
A recent survey lists practical tools and online systems for investigating semantic change of words over time. [12] WordEvolutionStudy is an academic platform that takes arbitrary words as input to generate summary views of their evolution based on Google Books ngram dataset and the Corpus of Historical American English. [13]
Central to what de Saussure says about words are two related statements: First, he says that "the sign is arbitrary". He considers the words that we use to indicate things and concepts could be any words – they are essentially just a consensus agreed upon by the speakers of a language and have no discernible pattern or relationship to the thing.
The INS officials, however, didn't take that as the final word. Instead, they sent a small team to the West Coast to continue investigating. The investigators later traveled to New York to depose ...
For example, polycyclic groups have solvable word problems since the normal form of an arbitrary word in a polycyclic presentation is readily computable; other algorithms for groups may, in suitable circumstances, also solve the word problem, see the Todd–Coxeter algorithm [8] and the Knuth–Bendix completion algorithm. [9]