PPT - UBC Department of CPSC Undergraduates
... Finishing the Proof Assume for contradiction that 2 is rational. Then, 2 = a/b for a Z, b Z+, where a and b have no common factor except 1. So, a2 = 2b2, and a2 is even. Since a2 is even, a is even (prev. proof!!). a = 2k for some integer k. b2 = a2/2 = (2k)2/2 = 2k2. b2 is even and so is b. ...
... Finishing the Proof Assume for contradiction that 2 is rational. Then, 2 = a/b for a Z, b Z+, where a and b have no common factor except 1. So, a2 = 2b2, and a2 is even. Since a2 is even, a is even (prev. proof!!). a = 2k for some integer k. b2 = a2/2 = (2k)2/2 = 2k2. b2 is even and so is b. ...
The Bene ts of Relaxing Punctuality1
... and less than 5:1 time units. We de ne a language that can constrain the time di erence between events only with nite, yet arbitrary, precision. This is accomplished by prohibiting singular time intervals, of the form [a; a], from constraining temporal operators. The resulting Metric Interval Tempo ...
... and less than 5:1 time units. We de ne a language that can constrain the time di erence between events only with nite, yet arbitrary, precision. This is accomplished by prohibiting singular time intervals, of the form [a; a], from constraining temporal operators. The resulting Metric Interval Tempo ...
On the structure of triangulated categories with finitely many
... obtain the same result with a new proof in section 4, namely that each connected component of the Auslander-Reiten quiver of the category T is of the form Z∆/G, where ∆ is a simply laced Dynkin diagram and G is trivial or a weakly admissible group of automorphisms. We are interested in the k-linear ...
... obtain the same result with a new proof in section 4, namely that each connected component of the Auslander-Reiten quiver of the category T is of the form Z∆/G, where ∆ is a simply laced Dynkin diagram and G is trivial or a weakly admissible group of automorphisms. We are interested in the k-linear ...
Document
... base is to be used as a factor. A number produced by raising a base to an exponent is called a power. 27 and 33 are ...
... base is to be used as a factor. A number produced by raising a base to an exponent is called a power. 27 and 33 are ...
Making Abstract Domains Condensing
... with respect to an operation ⊗, stating that for any pair of abstract objects a and b, the semantics S(a ⊗ b) can be retrieved as a ⊗ S(b). This generalizes and exactly captures the above notion of condensation when ⊗ is the abstract operation of unification. In particular, this also encompasses the ...
... with respect to an operation ⊗, stating that for any pair of abstract objects a and b, the semantics S(a ⊗ b) can be retrieved as a ⊗ S(b). This generalizes and exactly captures the above notion of condensation when ⊗ is the abstract operation of unification. In particular, this also encompasses the ...
Introduction to Linear Logic - Shane Steinert
... A morphism f ∈ hom(X , Y ) is an isomorphism if there is a g ∈ hom(Y , X ) such that fg = 1X and gf = 1y . Note that one can provide similar conditions for epi- and mono-morphisms which mirror standard cases of surjections and injections respectively. I only define isomorphisms here because we will ...
... A morphism f ∈ hom(X , Y ) is an isomorphism if there is a g ∈ hom(Y , X ) such that fg = 1X and gf = 1y . Note that one can provide similar conditions for epi- and mono-morphisms which mirror standard cases of surjections and injections respectively. I only define isomorphisms here because we will ...
