background preloader

Logica

Facebook Twitter

Funzione inversa. Da Wikipedia, l'enciclopedia libera. manda 3 in a poiché f manda a in 3 si dice invertibile se esiste una funzione tale che per ogni , e più formalmente, dove.

Funzione inversa

Omomorfismo. Da Wikipedia, l'enciclopedia libera. è un omomorfismo se vale per ogni coppia di elementi di , dove e sono le operazioni binarie di rispettivamente.

Omomorfismo

Ogni tipo di struttura algebrica ha i suoi specifici omomorfismi: Definizione[modifica | modifica sorgente] Una definizione rigorosa generale di omomorfismo può essere data nel modo seguente: Siano due strutture algebriche dello stesso tipo. È un omomorfismo se, per ogni operazione. König's lemma. König's lemma or König's infinity lemma is a theorem in graph theory due to Dénes Kőnig (1936).[1] It gives a sufficient condition for an infinite graph to have an infinitely long path.

König's lemma

The computability aspects of this theorem have been thoroughly investigated by researchers in mathematical logic, especially in computability theory. This theorem also has important roles in constructive mathematics and proof theory. Statement of the lemma[edit] Note that the vertex degrees must be finite, but need not be uniformly bounded: it is possible to have one vertex of degree 10, another of degree 100, a third of degree 1000, and so on. Proof[edit] For the proof, assume that the graph consists of infinitely many vertices and is connected. Start with any vertex v1. Now infinitely many vertices of G can be reached from v2 with a simple path which doesn't use the vertex v1. Continuing in this fashion, an infinite simple path can be constructed by mathematical induction. Is added to the finite set. to. Modal Logic. First published Tue Feb 29, 2000; substantive revision Fri Oct 2, 2009 A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement.

Modal Logic

Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’. However, the term ‘modal logic’ may be used more broadly for a family of related systems. These include logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as ‘it is obligatory that’ and ‘it is permitted that’, and many others.

An understanding of modal logic is particularly valuable in the formal analysis of philosophical argument, where expressions from the modal family are both common and confusing. 1. Narrowly construed, modal logic studies reasoning that involves the use of the expressions ‘necessarily’ and ‘possibly’. A list describing the best known of these logics follows. 2. Some paradoxes - an anthology. Richard's Paradox. Here are three paradoxes, all based on the same idea. 1.

Richard's Paradox

Let A be the set of all positive integers that can be defined in under 100 words. Since there are only finitely many of these, there must be a smallest positive integer n that does not belong to A. But haven't I just defined n in under 100 words? 2. 3. The solution to these paradoxes is usually explained as follows: they depend on being imprecise about what is meant by defining a number, or being interesting. To kill off the paradox completely, one has only to look at the argument in more detail. In words, sm(n) is the nth string that makes T-sense, and this notion itself makes T-sense because the function f is T-definable (by hypothesis) and hence so is g. xn is the real number defined by sm(n). Now I apply an explicit, T-definable, diagonal argument to the list x1,x2,x3,... obtaining the number y. 4.

What is the nth digit of y? Non solo matematica... Funzione di Ackermann. Da Wikipedia, l'enciclopedia libera. oppure: La funzione di Ackermann è un esempio di funzione ricorsiva che non è primitiva ricorsiva poiché cresce più velocemente di qualsiasi funzione ricorsiva primitiva.

Funzione di Ackermann

(mediante iterazione di per volte) (y volte)(mediante iterazione di volte e quindi mediante iterazione di e quindi mediante iterazione di Risulta quindi una funzione con una complessità estremamente elevata anche per valori di input semplici. Voci correlate[modifica | modifica sorgente]