define explanation

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These example sentences are selected automatically from various online news sources to reflect current usage of the word 'explanation.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

The notion of a function is easily understood using the metaphor of a function machine that takes in an object for its input and, based on that input, spits out another object as its output.
A function is more formally defined given a set of inputs $X$ (domain) and a set of possible outputs $Y$ (codomain) as a set of ordered pairs $(x,y)$ where $x in X$ (confused?) and $y in Y$, subject to the restriction that there can be only one ordered pair with the same value of $x$. We can write the statement that $f$ is a function from $X$ to $Y$ using the function notation $f: X to Y$.

The change had already happened which is the test and definition of evening.
This self-denial is the test and definition of self-government.

References:

http://mathinsight.org/definition/function
http://www.thesaurus.com/browse/definition
http://www.businessdictionary.com/definition/system.html