Mathematical Logic
... Definition 1.1.5. If A is a formula, the degree of A is the number of occurrences of propositional connectives in A. This is the same as the number of times rules 2 and 3 had to be applied in order to generate A. ...
... Definition 1.1.5. If A is a formula, the degree of A is the number of occurrences of propositional connectives in A. This is the same as the number of times rules 2 and 3 had to be applied in order to generate A. ...
preprint - Open Science Framework
... Subject can register not only what objects it has created so far but also how and when, and that this reflection can be exploited to demonstrate mathematical theorems. An example is Brouwer’s argument published in [10] to the conclusion that we have at present no evidence for ∀x ∈ R(x ≠ 0 → x # 0) ...
... Subject can register not only what objects it has created so far but also how and when, and that this reflection can be exploited to demonstrate mathematical theorems. An example is Brouwer’s argument published in [10] to the conclusion that we have at present no evidence for ∀x ∈ R(x ≠ 0 → x # 0) ...
On the non-existence of constants of derivations: the proof of a
... Trying to understand the second proof, we have gradually realized that the starting point of it relies on some very clever and general ideas, which can be applied to many other derivations, mainly but not exclusively to derivations where polynomials fi (see 1.4) are homogeneous polynomials of the s ...
... Trying to understand the second proof, we have gradually realized that the starting point of it relies on some very clever and general ideas, which can be applied to many other derivations, mainly but not exclusively to derivations where polynomials fi (see 1.4) are homogeneous polynomials of the s ...
Full text
... In one of his famous results, Fermat showed that there exists no Pythagorean triangle with integer sides whose area is an integer square. His elegant method of proof is one of the first known examples in the history of the theory of numbers where the method of infinite descent is employed. Mohanty [ ...
... In one of his famous results, Fermat showed that there exists no Pythagorean triangle with integer sides whose area is an integer square. His elegant method of proof is one of the first known examples in the history of the theory of numbers where the method of infinite descent is employed. Mohanty [ ...
Full text
... An integer m is a pronic number if m is the product of two consecutive integers. We shall show that the only Lucas number which is a product of two consecutive integers is LQ = 2. The author has been informed by the referee that the results of this paper appeared recently in a Chinese journal (in Ch ...
... An integer m is a pronic number if m is the product of two consecutive integers. We shall show that the only Lucas number which is a product of two consecutive integers is LQ = 2. The author has been informed by the referee that the results of this paper appeared recently in a Chinese journal (in Ch ...
Introduction to Linear Logic - Shane Steinert
... Set switches arbitrarily. Pick an arbitrary formula and exit gate at t = 0. By construction, there are clear, unambiguous directions on how to proceed indefinitely. Because this is a finite structure, however, every trip is periodic. Let k be the smallest positive integer such that the particle inte ...
... Set switches arbitrarily. Pick an arbitrary formula and exit gate at t = 0. By construction, there are clear, unambiguous directions on how to proceed indefinitely. Because this is a finite structure, however, every trip is periodic. Let k be the smallest positive integer such that the particle inte ...
![CS 512, Spring 2017, Handout 05 [1ex] Semantics of Classical](http://s1.studyres.com/store/data/001902216_1-d85c63c8a0994ab9df7b1ab59a6b4141-300x300.png)
Pythagorean triangles with legs less than n
... also 6nd a bound for the area of the curved triangle on the right. For that, taking into account the slope in the arc AB, it is easy to check √ that the curved triangle is always included in a right-angled triangle with legs ...
... also 6nd a bound for the area of the curved triangle on the right. For that, taking into account the slope in the arc AB, it is easy to check √ that the curved triangle is always included in a right-angled triangle with legs ...
Indecomposable permutations with a given number of cycles
... take as parameter the number of left-to-right maxima instead of the number of cycles, note that these two statistics are equal for general permutations. Similarly the above bijection associates to indecomposable involutions maps on orientable surfaces having the same number of vertices as the involu ...
... take as parameter the number of left-to-right maxima instead of the number of cycles, note that these two statistics are equal for general permutations. Similarly the above bijection associates to indecomposable involutions maps on orientable surfaces having the same number of vertices as the involu ...
Marian Muresan Mathematical Analysis and Applications I Draft
... (d) The set of rational numbers Q = {p/q | p, q ∈ Z, q 6= 0}; 3 (e) The set of positive integers less than 7; (f) The set of Romanian cities having more than five million of inhabitants; (g) The set S of vowels in English alphabet. S may be written as S = {a, e, i, o, u} or S = {x | x is a vowel in ...
... (d) The set of rational numbers Q = {p/q | p, q ∈ Z, q 6= 0}; 3 (e) The set of positive integers less than 7; (f) The set of Romanian cities having more than five million of inhabitants; (g) The set S of vowels in English alphabet. S may be written as S = {a, e, i, o, u} or S = {x | x is a vowel in ...
Mathematical proof
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed true is known as a conjecture.Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.