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  2. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    In approximate arithmetic, such as floating-point arithmetic, the distributive property of multiplication (and division) over addition may fail because of the limitations of arithmetic precision. For example, the identity 1 / 3 + 1 / 3 + 1 / 3 = ( 1 + 1 + 1 ) / 3 {\displaystyle 1/3+1/3+1/3=(1+1+1)/3} fails in decimal arithmetic , regardless of ...

  3. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    The order of operations emerged progressively over centuries. The rule that multiplication has precedence over addition was incorporated into the development of algebraic notation in the 1600s, since the distributive property implies this as a natural hierarchy.

  4. Casting out nines - Wikipedia

    en.wikipedia.org/wiki/Casting_out_nines

    This property is also preserved for the 'digit sum' where the base and the modulus differ by 1. If a calculation was correct before casting out, casting out on both sides will preserve correctness. However, it is possible that two previously unequal integers will be identical modulo 9 (on average, a ninth of the time).

  5. Addition - Wikipedia

    en.wikipedia.org/wiki/Addition

    Commutative property: Mentioned above, using the pattern a + b = b + a reduces the number of "addition facts" from 100 to 55. One or two more: Adding 1 or 2 is a basic task, and it can be accomplished through counting on or, ultimately, intuition. [36] Zero: Since zero is the additive identity, adding zero is trivial.

  6. Distributivity (order theory) - Wikipedia

    en.wikipedia.org/wiki/Distributivity_(order_theory)

    An element x is called a dual distributive element if ∀y,z: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z). In a distributive lattice, every element is of course both distributive and dual distributive. In a non-distributive lattice, there may be elements that are distributive, but not dual distributive (and vice versa).

  7. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    For a function (,,) in three-dimensional Cartesian coordinate variables, the gradient is the vector field: ⁡ = = (, , ) = + + where i, j, k are the standard unit vectors for the x, y, z-axes.

  8. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    A fundamental property of real numbers is that rational approximations are compatible with arithmetic operations, and, in particular, with multiplication. This means that, if a and b are positive real numbers such that a = sup x ∈ A x {\displaystyle a=\sup _{x\in A}x} and b = sup y ∈ B y , {\displaystyle b=\sup _{y\in B}y,} then a ⋅ b ...

  9. Distributive lattice - Wikipedia

    en.wikipedia.org/wiki/Distributive_lattice

    The simplest non-distributive lattices are M 3, the "diamond lattice", and N 5, the "pentagon lattice". A lattice is distributive if and only if none of its sublattices is isomorphic to M 3 or N 5; a sublattice is a subset that is closed under the meet and join operations of the original lattice. Note that this is not the same as being a subset ...

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