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A monoid ideal in a monoid A is a subset I that is multiplicatively closed, contains 0, and such that IA = {ra : r ∈ I, a ∈ A} = I. Such an ideal is prime if A ∖ I is multiplicatively closed and contains 1. For monoids A and B, a monoid homomorphism is a function f : A → B such that =; =, and
A graph is Hamiltonian if it contains a Hamiltonian cycle, and traceable if it contains a Hamiltonian path. haven A k-haven is a function that maps every set X of fewer than k vertices to one of its flaps, often satisfying additional consistency conditions.
Similarly, the geometric mean of n positive real numbers is an n-ary function: (=) = . Note that a logarithm of the geometric mean is the arithmetic mean of the logarithms of its n arguments From a mathematical point of view, a function of n arguments can always be considered as a function of a single argument that is an element of some product ...
Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly with different coefficients. More generally, when some variable are considered as parameters, like terms are defined similarly, but "numerical factors" must be replaced by "factors depending only on the parameters".
In the case of a multivariate function, the parentheses contain several expressions separated by commas, such as (,). 2. May also denote a product, such as in (+). When the confusion is possible, the context must distinguish which symbols denote functions, and which ones denote variables. ( , )
A synonym is a word, morpheme, or phrase that means precisely or nearly the same as another word, morpheme, or phrase in a given language. [2] For example, in the English language , the words begin , start , commence , and initiate are all synonyms of one another: they are synonymous .
Thesaurus Linguae Latinae. A modern english thesaurus. A thesaurus (pl.: thesauri or thesauruses), sometimes called a synonym dictionary or dictionary of synonyms, is a reference work which arranges words by their meanings (or in simpler terms, a book where one can find different words with similar meanings to other words), [1] [2] sometimes as a hierarchy of broader and narrower terms ...
The image of the limit of a contains a single point f(x), so it does not contain the limit of b. In contrast, that function is lower hemicontinuous everywhere. For example, for any sequence a that converges to x, from the left or from the right, f(x) contains a single point, and there exists a corresponding sequence b that converges to f(x).