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What is the symbol most commonly used for in a mathematical or math-related context?

  • LaTeX produces the symbol with \hateq.
  • The symbol has Unicode codepoint U+2259.
  • The respective Unicode code chart shows it with the name ESTIMATES and the annotation = corresponds to. Note that the names and annotations there are often not helpful, incomplete, or even misleading.
  • Entering it into the English Wikipedia currently redirects to the article Correspondence (mathematics).

Where and how is used in math or related fields? (By "related" I am thinking of statistics and physics.)

I believe to remember that I have seen it in some sort of "correspondence" meaning in a college-level science class.

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The hat above the equals sign is an estimator. Originaly estimators are used on terms. For example:

$$\widehat{\theta}(X)$$

But it has appeared (sometimes) more convenient to use it with an equals sign, especially in statistics. It has transformed a substantive (θ is an estimator for . . .) into a verb.

x ≙ . . . then reads as x estimates . . .

You use it instead of a plain equals sign when you do not have a strict equality between the left term and the right expression. Statistically speaking, it symbolizes an estimation of an unobservable quantity.

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In statistics, it is to define the sample minimum $x_{(1)}$ or sample maximum $x_{(n)}$.

For example,

$$x_{(1)} ≙ min\{x_1, x_2, ..., x_n\}$$

$x_{(1)}$ is also called the smallest observation.

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  • $\begingroup$ You didn't explain why this usage is different from a plain equals ("$=$") sign. $\endgroup$ – fonini Feb 1 '15 at 2:36
  • $\begingroup$ I can see there is no too much difference except that it just emphasizes this is a definition. $\endgroup$ – canoe Feb 1 '15 at 2:48

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