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Tilde


The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In informal usage, "tilde" is often instead voiced as "twiddle" (Derbyshire 2004, p. 45).

1. An operator such as the differential operator D^~.

2. The statistical median x^~ (Kenney and Keeping 1962, p. 211).

The tilde is sometimes used as its own symbol.

1. In asymptotic notation, f∼phi is used to mean that f/phi->1.

2. Physicists and astronomers use same notation to mean "f is of the same order of magnitude as phi."

3. In set theory, x∼y means that there is an equivalence relation between x and y.

4. In statistics, the tilde is frequently used to mean "has the distribution (of)," for instance, X∼N(0,1) means "the stochastic (random) variable X has the distribution N(0,1) (the standard normal distribution). If X and Y are stochastic variables then X∼Y means "X has the same distribution as Y.


See also

Asymptotic Notation, Differential Operator, Equivalence Relation, Order of Magnitude, Statistical Median

Portions of this entry contributed by Peter Acklam

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References

Bringhurst, R. The Elements of Typographic Style, 2nd ed. Point Roberts, WA: Hartley and Marks, p. 284, 1997.Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. New York: Penguin, 2004.Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 1962.

Referenced on Wolfram|Alpha

Tilde

Cite this as:

Acklam, Peter and Weisstein, Eric W. "Tilde." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Tilde.html

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