Split out of #596, where @Happypig375 asked: "how to make codomains unified with provided node with the in relation?"
The two look like the same test and are not quite.
MathS.Settings.Codomain is a statement about where the function is being read -- real-valued or complex-valued.provided x in RR is a statement about the point.
lim x->0- (x^x) is a limit at a real point of a function that is not real-valued anywhere to the left of it. So the predicate x in RR holds and tells you nothing, while the codomain is what rules the limit out. Unifying them means reading the condition as a claim about the neighbourhood rather than the point -- which is probably what is meant, and is a real change rather than an alias.
Worth doing: a single notion would mean expr provided x in RR and Codomain = RR cannot drift apart, and it would let a domain be stated locally rather than as a global setting. But it is wider than reading MathS.Settings.Codomain in ComputeLimit, which is why the sibling issue does the narrow thing first.
Filed so the question is not lost inside #596.
Split out of #596, where @Happypig375 asked: "how to make codomains unified with provided node with the in relation?"
The two look like the same test and are not quite.
MathS.Settings.Codomainis a statement about where the function is being read -- real-valued or complex-valued.provided x in RRis a statement about the point.lim x->0- (x^x)is a limit at a real point of a function that is not real-valued anywhere to the left of it. So the predicatex in RRholds and tells you nothing, while the codomain is what rules the limit out. Unifying them means reading the condition as a claim about the neighbourhood rather than the point -- which is probably what is meant, and is a real change rather than an alias.Worth doing: a single notion would mean
expr provided x in RRandCodomain = RRcannot drift apart, and it would let a domain be stated locally rather than as a global setting. But it is wider than readingMathS.Settings.CodomaininComputeLimit, which is why the sibling issue does the narrow thing first.Filed so the question is not lost inside #596.