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In a category with all finite limits and colimits, the image is defined as the equalizer (,) of the so-called cokernel pair (,,), which is the cocartesian of a morphism with itself over its domain, which will result in a pair of morphisms ,:, on which the equalizer is taken, i.e. the first of the following diagrams is cocartesian, and the second equalizing.
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The image of the function is the set of all output values it may produce, that is, the image of . The preimage of f {\displaystyle f} , that is, the preimage of Y {\displaystyle Y} under f {\displaystyle f} , always equals X {\displaystyle X} (the domain of f {\displaystyle f} ); therefore, the former notion is rarely used.
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By reflecting the "billiard table" we can visualize the path as a straight line. In this example the ratio of the two given numbers is 2/3. There are a few ways to show a proof of arithmetic billiards. Consider a square with side (,). By displaying multiple copies of the original rectangle (with mirror symmetry) we can visualise the ...
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