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I guess that's why he talks about applications and not functions, so that guarantees there is a single x for each y.
by wott 10y ago
I guess that's why he talks about applications and not functions, so that guarantees there is a single x for each y.
- deleted 10y ago[deleted]
- mannykannot 10y agoI think he was just clarifying a point about the notation. Given that each f is a function, mapping each member of its domain to one member of its range, and that for each member of the range, there is a member of the domain that the given function maps to it, and that the domain and range are the same size, then there can be no member of the domain not mapped to some member of the range, and each member of the domain must be mapped to a distinct member of the range (or else there would not be enough members of the domain to cover all the members of the range), so, with the domain and range being the same set, each of the given functions is a permutation of the domain, and collectively they must be all of them. This is a verbose version of the argument for this being the set the author says it is. Arguably, it would be easier to read if I had used x for 'member of the domain', y for 'member of the range' and f for 'the given function'.