In most programming languages, mentioning an object inside it's definition can cause a lot of trouble at compile time because what's being mentioned doesn't technically exist yet.(adsbygoogle = window.adsbygoogle || []).push({});

But in mathematics is "forward referencing" allowed? Can I, for instance, define a set and use the set being defined in the definition??

For example, using set builder notation:

S = {x in X : P(x)}.

Where the formula P makes mention of S? Like,

S = {(a,b) in AxB : for all b' [((a,b) in S and (a,b') in S) => (b = b')]}.

Is that allowed in mathematics? If not, is there always a way to define things not mentioning them? In the case of the functional relation above, how would I do it?

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# Forward referencing in mathematics

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