Sentence examples for multiplication is defined from inspiring English sources

From the above laws, it is evident that a repeated sum such as 5 + 5 + 5 is independent of the way in which the summands are grouped; it can be written 3 × 5. Thus, a second binary operation called multiplication is defined.

Then the multiplication is defined by (2.6).

(i) A0 is dense in A with respect to its norm || · ||; (ii) (ab)* = b*a* whenever the multiplication is defined; (iii) || y ||0= supa ∈ A, || a ||≤1|| ay || for all y ∈ A0.

That is, A is a real Banach space in which an operation of multiplication is defined, subject to the following properties (for all x, y, z ∈ A, α ∈ R ): 1. ( x y ) z = x ( y z ) ;   2.

That is, is a real Banach space in which an operation of multiplication is defined, subject to the following properties (for all x, y, z ∈ A, α ∈ R ): 1. ( x y ) z = x ( y z ) ;   2.

That is, A is a real Banach space in which an operation of multiplication is defined subject to the following properties (for all (x, y, zin A), (alphain R)): 1. ((xy z=x yz));   2.

In particular the marks may be taken to be the set X of non-negative integers less than a prime p. If this is so, then addition and multiplication are defined by modified addition and multiplication laws in which a, b, r, and p belong to X.

The operation of multiplication was defined to be intersection, and this led to his first law, xy = yx.

Let S be the space of real numbers, then ℑ(X) is a linear space over the field S where the addition and scalar multiplication are defined by f + g = { ( x, μ ) + ( y, η ) } = { ( x + y, μ ∧ η ) : ( x, μ ) ∈ f and ( y, η ) ∈ g }. and λ f = { ( λ x, μ ) : ( x, μ ) ∈ f }.

(3) For two convex set-valued mappings T and (S : mathbb{R}^{l} rightrightarrowsmathbb{R}^{m}), addition and multiplication are defined by (T+S x=Tx+Sx,qquad (lambda T x=lambda(Tx) for all (xinmathbb{R}^{l} ) and (lambdainmathbb{R}), respectively.

A matrix is a rectangular array of numbers or other mathematical objects, for which operations such as addition and multiplication are defined.