In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help...

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity...

example, formally (i.e. by abuse of notation, since it is not straightforward to take a functional square root of the sum of two differential operators)...

x {\displaystyle x} alone, as in the study of Taylor series. By a slight abuse of notation, monomials of shifted variables, for instance 2 x ¯ 3 = 2...

Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual...

be a function". This is an abuse of notation that is useful for a simpler formulation. Arrow notation defines the rule of a function inline, without requiring...

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling...

Look up notation system in Wiktionary, the free dictionary. In linguistics and semiotics, a notation system is a system of graphics or symbols, characters...

the whole space X. This abuse of notation is, in fact, taken to be perfectly normal in measure theory; it is the standard notation for the Radon–Nikodym...

F = 0. {\displaystyle Q(x,y)=Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0.} By an abuse of notation, this conic section will also be called Q {\displaystyle Q} when no...

components of F, and sum the results. Because applying an operator is different from multiplying the components, this is considered an abuse of notation. For...

is unimportant, and in a simplifying abuse of notation, the indexed family can be treated simply as a collection of sets. In this case A i ∗ {\displaystyle...

{\mathcal {P}}(X),} the power set of X. Consequently, both sets are denoted by the conventional abuse of notation as 2 X , {\displaystyle 2^{X},} in...

function when it points in the "true direction" of the flow. (Strictly speaking, this is an abuse of notation because the "arg max" cannot directly compare...

sometimes called the "local basis". This definition allows a common abuse of notation. The ∂ i {\displaystyle \partial _{i}} were defined to be in one-to-one...

Look up up to in Wiktionary, the free dictionary. Abuse of notation Adequality Essentially unique List of mathematical jargon Modulo (jargon) Quotient group...

∇f(a). Consequently, the gradient produces a vector field. A common abuse of notation is to define the del operator (∇) as follows in three-dimensional...

\rightarrow \mathbf {C} } over a field F is defined as (somewhat of an abuse of notation) R ( ϕ / F ) = min { r | ∃ f i ∈ A ∗ , g i ∈ B ∗ , w i ∈ C , ∀...

involve multiplying a single pair of group elements, not "adding" group elements. This is an abuse of notation, since element of matrices being multiplied must...

of a formula Φ {\displaystyle \Phi } may be written with a little abuse of notation as ∃ M ∃ μ ( M , μ ⊨ Φ ) {\displaystyle \exists M\exists \mu (M,\mu...

{\displaystyle V} are the positive elements of W , {\displaystyle W,} by abuse of notation. This implies that for a C*-algebra, a positive linear functional sends...

inverse of its transpose coincides with the canonical injection of ℓq into its double dual. As a consequence ℓq is a reflexive space. By abuse of notation, it...

\varphi ^{-1})}{\partial x^{\mu }}}.} The definition of the cotetrad uses the usual abuse of notation d x μ = d φ μ {\displaystyle dx^{\mu }=d\varphi ^{\mu...

equation E = mc2 includes a term for the speed of light squared. This led over time to an "abuse of notation" whereby superscripts indicate iterative function...

adjunction). The use of the equals sign is an abuse of notation; those two groups are not really identical but there is a way of identifying them that...

Science The text "1cm = 6km" is an abuse of notation for the equals sign; strictly, 1 cm=0.00001 km, as per definition of the metric prefixes. Snyder, John...

a^{-1}{\pmod {m}},} but this can be considered an abuse of notation since it could be misinterpreted as the reciprocal of a {\displaystyle a} (which, contrary to...

|\mu |=\mu ^{+}+\mu ^{-}} The last measure is sometimes called, by abuse of notation, total variation measure. If the measure μ {\displaystyle \mu } is...

this is an abuse of notation, by analogy with C k {\displaystyle C^{k}} and C ∞ {\displaystyle C^{\infty }} ), and then spaces of germs of (finitely)...

}f(x)\,\delta (x)\,dx=f(0)} holds. As a result, the latter notation is a convenient abuse of notation, and not a standard (Riemann or Lebesgue) integral. As...