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2. De Morgan's laws - Wikipedia

   en.wikipedia.org/wiki/De_Morgan's_laws

   De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.

3. Serre's multiplicity conjectures - Wikipedia

   en.wikipedia.org/wiki/Serre's_multiplicity...

   Let R be a Noetherian, commutative, regular local ring and let P and Q be prime ideals of R. Serre defined the intersection multiplicity of R / P and R / Q by means of their Tor functors . Below, ℓ R ( M ) {\displaystyle \ell _{R}(M)} denotes the length of the module M {\displaystyle M} , and we assume for the remainder of the article that

4. List of incomplete proofs - Wikipedia

   en.wikipedia.org/wiki/List_of_incomplete_proofs

   3)−4 nodes, B. Segre pointed out that this was wrong; for example, for degree 6 the maximum number of nodes is 65, achieved by the Barth sextic, which is more than the maximum of 52 claimed by Severi. Rokhlin invariant. Rokhlin incorrectly claimed in 1951 that the third stable stem of the homotopy groups of spheres is of order 12. In 1952 he ...

5. Intersection number - Wikipedia

   en.wikipedia.org/wiki/Intersection_number

   The complexity enters when calculating intersections at points of tangency, and intersections which are not just points, but have higher dimension. For example, if a plane is tangent to a surface along a line, the intersection number along the line should be at least two. These questions are discussed systematically in intersection theory.

6. List of set identities and relations - Wikipedia

   en.wikipedia.org/wiki/List_of_set_identities_and...

   In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).

7. Bézout's theorem - Wikipedia

   en.wikipedia.org/wiki/Bézout's_theorem

   An intersection point is said isolated if it does not belong to a component of positive dimension of the intersection; the terminology make sense, since an isolated intersection point has neighborhoods (for Zariski topology or for the usual topology in the case of complex hypersurfaces) that does not contain any other intersection point.