On Wednesday, November 1, 2017 at 8:22:09 AM UTC+1, ruben safir wrote: > On 10/30/2017 12:25 PM, Arturo Magidin wrote: > > A function f:D->E is "constant" if for any x and y in D, f(x)=f(y). > > > > It doesn't matter what the domain (or codomain) are; it just means any > > two inputs give the same output. > > that would mean that all x,y combinations (an entire plane) is valid > points in a graph of such a constant function?
DxD would be "the entire plane" only if D is "the entire line": what and all that is required is that x and y *in D*, i.e. in the domain of the function, such that f(x) and f(y) are in fact defined (and just equal to a constant in our case).