Bijection: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "A bijection between two sets, \(X\) and \(Y\), is a "one-to-one pairing" of their elements. Formally, it is a function \(f: X \to Y\) (which can be encoded as a subset of \(X \times Y\)) so that: * Different elements of \(X\) are sent to different elements of \(Y\). * Every element of \(Y\) has some element of \(X\) which is sent to \(Y\). The first property is known as injectivity, or being 1-1, and can be formally be written as \(f(x) = f(y)\) only if \(x = y\). The...") |
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A bijection between two sets, \(X\) and \(Y\), is a "one-to-one pairing" of their elements. Formally, it is a function \(f: X \to Y\) (which can be encoded as a subset of \(X \times Y\)) so that:
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