Algorithmic Number Theory
... Fact 2.1 The following are easy to show. 1. 1|a for all a ∈ Z, 2. a|a for all a 6= 0, 3. a|b implies a|bc, for all c ∈ Z, 4. a|b and b|c implies a|c, 5. a|b and a|c implies a|b ± c, 6. Every prime is a positive integer. 2 is the smallest prime. Theorem 2.2 The set of primes is infinite. Proof outlin ...
... Fact 2.1 The following are easy to show. 1. 1|a for all a ∈ Z, 2. a|a for all a 6= 0, 3. a|b implies a|bc, for all c ∈ Z, 4. a|b and b|c implies a|c, 5. a|b and a|c implies a|b ± c, 6. Every prime is a positive integer. 2 is the smallest prime. Theorem 2.2 The set of primes is infinite. Proof outlin ...
CLASSICAL BI: ITS SEMANTICS AND PROOF THEORY 1
... units and whose internal nodes are either semicolons or commas. The crucial difference between the latter two operations is that weakening and contraction are possible for the additive semicolon but not for the multiplicative comma. Since BI is intuitionistic in both its additive and multiplicative ...
... units and whose internal nodes are either semicolons or commas. The crucial difference between the latter two operations is that weakening and contraction are possible for the additive semicolon but not for the multiplicative comma. Since BI is intuitionistic in both its additive and multiplicative ...
![arXiv:math/0204351v1 [math.DG] 30 Apr 2002](http://s1.studyres.com/store/data/014313402_1-a36470e1d30219061b5b11239e80d15a-300x300.png)
BARENDREGT`S LEMMA Dedicated to Henk Barendregt, in
... to formulate as it is to prove. As to the quoted proof, “Same method as the proof of 9” says so much as: by the method used earlier in the paper, which used a variant of underlining. I am not sure, but I think the note dates from 1972. A few years later, I was working in Eindhoven at that time, I st ...
... to formulate as it is to prove. As to the quoted proof, “Same method as the proof of 9” says so much as: by the method used earlier in the paper, which used a variant of underlining. I am not sure, but I think the note dates from 1972. A few years later, I was working in Eindhoven at that time, I st ...
Week 7: Limits at Infinity. - MA161/MA1161: Semester
... Continuity on an Interval. We say that a function f : D → R is continuous, if it is continuous at all points in its domain D. If the domain D consists of intervals, this means that the function needs to be continuous on each interval, in the following sense. A function f : D → R is continuous on an ...
... Continuity on an Interval. We say that a function f : D → R is continuous, if it is continuous at all points in its domain D. If the domain D consists of intervals, this means that the function needs to be continuous on each interval, in the following sense. A function f : D → R is continuous on an ...
Full text
... of n. So one can say if A = (Ai • • • Aj) is an r-subcomplete partition of n then each number between — rn and rn can be represented by the form. We will need this simple fact in the proof of Lemma 2.9 and Theorem 2.10. The following Lemma shows that every r-subcomplete partition should have 1 as th ...
... of n. So one can say if A = (Ai • • • Aj) is an r-subcomplete partition of n then each number between — rn and rn can be represented by the form. We will need this simple fact in the proof of Lemma 2.9 and Theorem 2.10. The following Lemma shows that every r-subcomplete partition should have 1 as th ...
Sequential Dynamic Logic
... This property will be reflected in our calculus by extending the notion of a static proposition to all negated formulas. Note also that, when restricted to static propositions, ∼ behaves exactly as a classical negation. In particular, this implies that, like an intuitionistic negation, the dynamic ...
... This property will be reflected in our calculus by extending the notion of a static proposition to all negated formulas. Note also that, when restricted to static propositions, ∼ behaves exactly as a classical negation. In particular, this implies that, like an intuitionistic negation, the dynamic ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.