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The tilde can indicate approximate equality in a variety of ways. It can be used to denote the asymptotic equality of two functions. For example, f (x) ~ g (x) means that () =. [13] A tilde is also used to indicate "approximately equal to" (e.g. 1.902
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
The symbol ~ is the tilde. The relation is an equivalence relation on the set of functions of x; the functions f and g are said to be asymptotically equivalent. The domain of f and g can be any set for which the limit is defined: e.g. real numbers, complex numbers, positive integers.
The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.); The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it;
Functional notation: if the first is the name (symbol) of a function, denotes the value of the function applied to the expression between the parentheses; for example, (), (+). In the case of a multivariate function , the parentheses contain several expressions separated by commas, such as f ( x , y ) {\displaystyle f(x,y)} .
˜ ! ′ \lnot or \neg \sim ′ ' negation: not propositional logic, Boolean algebra: The statement is true if and only if A is false. A slash placed through another operator is the same as placed in front.
Most symbols denote functions or operators. A monadic function takes as its argument the result of evaluating everything to its right. (Moderated in the usual way by parentheses.) A dyadic function has another argument, the first item of data on its left. Many symbols denote both monadic and dyadic functions, interpreted according to use.
Evidently, conformality of metrics is an equivalence relation. Here are some formulas for conformal changes in tensors associated with the metric. (Quantities marked with a tilde will be associated with ~, while those unmarked with such will be associated with .)