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Equating these two formulas for the number of edge sequences results in Cayley's formula: ! =! and =. As Aigner and Ziegler describe, the formula and the proof can be generalized to count the number of rooted forests with k {\displaystyle k} trees, for any k {\displaystyle k} .
The condition is evaluated true or false as a Boolean expression. On the basis of the evaluation of the Boolean condition, the entire expression returns value_if_true if condition is true, but value_if_false otherwise. Usually the two sub-expressions value_if_true and value_if_false must have the same type, which determines the type of the ...
The checking is extremely fast, but has been limited to 500 instances per page because it is considered an "expensive parser function". (However, multiple checks of the same title on the same page do not count as multiple instances, because the results of the first check is cached and reused for the subsequent checks.)
The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
condition: An expression which is evaluated as a boolean value. expression 1, expression 2: Expressions with values of any type. If the condition is evaluated to true, the expression 1 will be evaluated. If the condition is evaluated to false, the expression 2 will be evaluated.
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Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.