As noted above, this may not always be possible. We will therefore fix a point (a, b) = ("a1", ..., "an", "b"1, ..., "bm") which satisfies "f"(a, b) = 0, and we will ask for a "g" that works near the point (a, b). In other words, we want an open set formula_9 containing a, an open set formula_10 containing b, and a function "g" : "U" → "V" such that the graph of "g" satisfies the relation "f" = 0 on "U" × "V", and that no other points within "U" × "V" do so. In symbols,