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The functions are simple data validation and data type checking functions. The data validation functions determine whether it is possible to convert or coerce the data value given as an argument to the function to the type implied by the function name, and return a Boolean value recording whether it was possible or not.
In technical terms, this means that the set of events and the three operations together constitute a Boolean algebra of sets, with an associated probability function. In standard practice, P(if A, then B) is not interpreted as P(A′ ∪ B), following the rule of material implication, but rather as the conditional probability of B given A, P(B ...
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...
See also: the {{}} template. The #if function selects one of two alternatives based on the truth value of a test string. {{#if: test string | value if true | value if false}} As explained above, a string is considered true if it contains at least one non-whitespace character.