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== Function spaces ==
The set of all partial functions <math>f : X \rightharpoonup Y</math> from a set <math>X</math> to a set <math>Y,</math> denoted by <math>[X \rightharpoonup Y],</math>{{cn|reason=3 different notations have been proposed recently by different Wikipedia editors, viz. "X→Y", "[X→Y]", and "{X→Y}". Only those that are supported by citations should be kept (resp. added to the current version).}} is the union of all functions defined on subsets of <math>X</math> with same codomain <math>Y</math>:
: <math>[X \rightharpoonup Y] = \bigcup_{D \subseteq{X}} [D \to Y],</math>
the latter also written as <math display="inline">\bigcup_{D\subseteq{X}} Y^D.</math> In finite case, its cardinality is
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