When defining the notion of injectivity of functions it uses notation, for example for a function [itex]f[/itex], [itex]f(a_{1})=f(a_{2})[/itex] where [itex]a_{1},a_{2}[/itex] are in the domain of the function. Since the empty set function, i.e., [itex]\emptyset \subseteq \emptyset \times A[/itex] for some set [itex]A[/itex], has the empty domain, the notation [itex]\emptyset (a)[/itex] is undefined, therefore the notion of injectivity is undefined. The reason why I'm concerned with this is that most textbooks when defining the notion of injectivity of functions do not specify the domains of the functions. Let me summarize my question:(adsbygoogle = window.adsbygoogle || []).push({});

Is the notion of injectivity undefined for the empty set function?

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# The notion of injectivity is undefined on the empty set function?

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