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The monomial basis also forms a basis for the vector space of polynomials. After all, every polynomial can be written as a 0 + a 1 x 1 + a 2 x 2 + ⋯ + a n x n {\displaystyle a_{0}+a_{1}x^{1}+a_{2}x^{2}+\cdots +a_{n}x^{n}} for some n ∈ N {\displaystyle n\in \mathbb {N} } , which is a linear combination of monomials.
An antonym is one of a pair of words with opposite meanings. Each word in the pair is the antithesis of the other. A word may have more than one antonym. There are three categories of antonyms identified by the nature of the relationship between the opposed meanings.
This is not sharp; the gap between the functions is everywhere at least 1. Among the exponential functions of the form α x, setting α = e 2/e = 2.0870652... results in a sharp upper bound; the slightly smaller choice α = 2 fails to produce an upper bound, since then α 3 = 8 < 3 2. In applied fields the word "tight" is often used with the ...
2. Denotes the additive inverse and is read as minus, the negative of, or the opposite of; for example, –2. 3. Also used in place of \ for denoting the set-theoretic complement; see \ in § Set theory. × (multiplication sign) 1. In elementary arithmetic, denotes multiplication, and is read as times; for example, 3 × 2. 2.
The last of the non-avian dinosaurs died 66 million years ago in the course of the Cretaceous–Paleogene extinction event, whereas the earliest members of the genus Homo (humans) evolved between 2.3 and 2.4 million years ago. This places a 63-million-year expanse of time between the last non-avian dinosaurs and the earliest humans.
Every vector a in three dimensions is a linear combination of the standard basis vectors i, j and k.. In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. [1]
In mathematics, the Yoneda lemma is a fundamental result in category theory. [1] It is an abstract result on functors of the type morphisms into a fixed object.It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms).
Exponential functions with bases 2 and 1/2 In mathematics , the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. The exponential of a variable x {\displaystyle x} is denoted exp x {\displaystyle \exp x} or e x {\displaystyle e^{x}} , with the two ...