On Feb 8, 11:25 am, "T.H. Ray" <thray...@aol.com> wrote: > Marshall wrote > > > > > On Feb 8, 4:15 am, "T.H. Ray" <thray...@aol.com> > > wrote: > > > Ostap Bender wrote > > > > > BTW, why do you like the term "to transform" so > > much? > > > > "To transform" > > > > means "to change", doesn't it? Do all functions > > > > actually change their > > > > domains? I just don't see that as a good > > metaphor. > > > > It isn't a metaphor at all. It's a property that > > > inheres in every function. It's a necessary > > condition. > > > The range of values within the domain have to obey > > > a relation between sets that defines the function. > > > This relation, what is it? I would assume it is a set > > of ordered pairs. The function, what is it? I would > > assume it is a set of ordered pairs. The same set, > > even. So what is the distinction? > > Answer this: is every set of ordered pairs a function? > Why or why not?
No, not every set of ordered pairs is a function. Only those sets of ordered pairs for which each "left" element of the set appears appears as a left element exactly once is a function.
Is that all we're talking about? Single-valued vs. multi-valued?