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The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as: [2] [5] Parentheses; Exponentiation; Multiplication and division; Addition and subtraction
The order of sequence of atomic orbitals (according to Madelung rule or Klechkowski rule) can be remembered by the following. [2] Order in which orbitals are arranged by increasing energy according to the Madelung rule. Each diagonal red arrow corresponds to a different value of n + l.
In mathematics, and more specifically in order theory, several different types of ordered set have been studied. They include: Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise; Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound.
The order of reactivity, as shown by the vigour of the reaction with water or the speed at which the metal surface tarnishes in air, appears to be Cs > K > Na > Li > alkaline earth metals, i.e., alkali metals > alkaline earth metals, the same as the reverse order of the (gas-phase) ionization energies.
An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
The first two in the sequence are by far the most common; 'tertiary' appears occasionally, and higher numbers are rare except in specialized contexts ('quaternary period'). The Greek series proto- , deutero- , trito- , ... is only found in prefixes, generally scholarly and technical coinages, e.g. protagonist, deuteragonist, tritagonist ...
The converse of this implication leads to functions that are order-reflecting, i.e. functions f as above for which f(a) ≤ f(b) implies a ≤ b. On the other hand, a function may also be order-reversing or antitone, if a ≤ b implies f(a) ≥ f(b). An order-embedding is a function f between orders that is both order-preserving and order ...