As a consequence this theorem has not received the attention it deserves. We give a simpler and shorter proof of this result as well as several restatements that are of independent interest. In addition, we mention applications to even-cycle matroids, even-cut matroids and frame matroids....
The de Rham theorem for general spaces The topological invariance of the de Rham groups suggests that there should be some purely topological way of computing them. There is indeed, and the connection between the de Rham groups and topology was first proved by Georges de Rham... JW Smith -...
The intent of this paper is to give a different proof which resembles a more naive way of approaching this theorem. LetI(T, λ)= the number of nonisomorphic models ofTin cardinalityλ. We prove: Theorem 0.1.If T is a complete countable first order theory then for 0<κ<λ, I(T,K) ...
which corresponds to P by the first isomorphism theorem. Then |P| = |P/N| · |N| = p k−1 · p = p k , so that P is a Sylow p-subgroup of G as desired. Theorem (Sylow’s Second Theorem). If G is a finite group and p is a prime ...
I shall first retell briefly how Heyting and Gentzen formulated their ideas and how others have taken them. In particular, I shall consider how the ideas have been or can be developed so that they become sufficiently precise and general to allow a meaningful comparison, which will then be ...
Theorem. Let a and b be elements of any ordered ring. Then |a + b| \leq |a| + |b|. Proof. By the definition of absolute value, it suffices to show that a + b \leq |a| + |b| and -(a + b) \leq |a| + |b|. The first claim follows from the fact that a \leq |...
Prove the theorem: F = \frac{r}{|r|^P} = \frac{\langle x, y, z \rangle}{(x^2 + y^2 +z^2)^{\frac{P}{2} is \nabla.F = \frac{3 - P}{|r|^P} How can you prove isomorphisms? 1. Prove that if f(x) = 10x + 16, ...
By appealing to the simplicial approximation theorem [2, p. 64] it suffices to prove that there is no simplicial retraction of a subdivision of a closed ra-simplex E onto its boundary dE. Suppose/: —>d is a simplicial retraction. Let a be the barycenter of an (n— l)-simplex A Ed...
Although both of them are rather successful, they suffer from their own deficiencies-that is, model checking is superior in checking a finite system automatically; theorem proving however can reason about systems with massive or infinite state spaces. In the thesis we present an embedding of the ...
a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian. In ...