Lecture Notes for the whole course

... Assume we want to arrange n objects in a line, the n objects are of k diﬀerent types, and objects of the same type are indistinguishable. Let ai be the number of objects of type i . Then the number of diﬀerent arrangements is: n! a1 !a2 ! . . . ak ! ...

... Assume we want to arrange n objects in a line, the n objects are of k diﬀerent types, and objects of the same type are indistinguishable. Let ai be the number of objects of type i . Then the number of diﬀerent arrangements is: n! a1 !a2 ! . . . ak ! ...

NORMALITY OF NUMBERS GENERATED BY THE VALUES OF

... is normal in base 10. These examples correspond to the choice f (x) = x in (1.1). Davenport and Erdös [5] considered the case where f (x) is a polynomial whose values at x = 1, 2, . . . are always integers and showed that in this case the numbers θq (f ) and τq (f ) are normal. For f (x) a polynomi ...

... is normal in base 10. These examples correspond to the choice f (x) = x in (1.1). Davenport and Erdös [5] considered the case where f (x) is a polynomial whose values at x = 1, 2, . . . are always integers and showed that in this case the numbers θq (f ) and τq (f ) are normal. For f (x) a polynomi ...

Graphical Representation of Canonical Proof: Two case studies

... of freely permutable inferences. A proof system that is free of bureaucracy is called canonical for a logic. In this dissertation two canonical proof systems are presented, for two logics: a notion of proof nets for additive linear logic with units, and ‘classical proof forests’, a graphical formali ...

... of freely permutable inferences. A proof system that is free of bureaucracy is called canonical for a logic. In this dissertation two canonical proof systems are presented, for two logics: a notion of proof nets for additive linear logic with units, and ‘classical proof forests’, a graphical formali ...

Announcement as effort on topological spaces

... 3Kϕ again means that the agent comes to know ϕ, but in the interpretation that there is a formula ψ such that after announcing it the agent knows ϕ. What becomes true or known by an agent after an announcement can be expressed in this language without explicit reference to the announced formula. Cle ...

... 3Kϕ again means that the agent comes to know ϕ, but in the interpretation that there is a formula ψ such that after announcing it the agent knows ϕ. What becomes true or known by an agent after an announcement can be expressed in this language without explicit reference to the announced formula. Cle ...

Diskrete Mathematik für Informatik (SS 2017)

... taking a practical look at the formal nuts and bolts of mathematical reasoning. ...

... taking a practical look at the formal nuts and bolts of mathematical reasoning. ...

Principia Logico-Metaphysica (Draft/Excerpt)

... A constant is any expression that is either an individual constant or an n-place relation constant (n 0). A variable is any expression that is either an individual variable or an n-place relation variable (n 0). The expressions listed in the column labeled ‘Less Formal’ are often used as replacement ...

... A constant is any expression that is either an individual constant or an n-place relation constant (n 0). A variable is any expression that is either an individual variable or an n-place relation variable (n 0). The expressions listed in the column labeled ‘Less Formal’ are often used as replacement ...

Introduction to Computational Logic

... This time the claim involves a boolean variable x and the proof proceeds by case analysis on x. Since reflexivity performs simplification automatically, we have omitted the tactic simpl. It is important that with Coq you step back and forth in the proof script and observe what happens. This way you ...

... This time the claim involves a boolean variable x and the proof proceeds by case analysis on x. Since reflexivity performs simplification automatically, we have omitted the tactic simpl. It is important that with Coq you step back and forth in the proof script and observe what happens. This way you ...

Title: Asymptotic distribution of integers with certain prime

... 2.2. Ordinal counting functions. It might seem surprising at first sight that the counting function M2,2 is related to studying asymptotic properties of transfinite ordinals. Since transfinite ordinals rarely show up in a number-theoretic context we will explain some features of this connection in i ...

... 2.2. Ordinal counting functions. It might seem surprising at first sight that the counting function M2,2 is related to studying asymptotic properties of transfinite ordinals. Since transfinite ordinals rarely show up in a number-theoretic context we will explain some features of this connection in i ...