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Lecture 2 – Proof Techniques
Lecture 2 – Proof Techniques

1 Proof by Contradiction - Stony Brook Mathematics
1 Proof by Contradiction - Stony Brook Mathematics

... show that we can write arbitrary sums without parentheses (a priori the associativity axiom only tells us this for sums of 3 terms). The reader is invited to revisit that proof. We now prove Theorem 4, that one of the players in Chomp has a winning strategy. To this end we define a valid Chomp posit ...
ordinal logics and the characterization of informal concepts of proof
ordinal logics and the characterization of informal concepts of proof

Slides
Slides

Proof Theory - Andrew.cmu.edu
Proof Theory - Andrew.cmu.edu

Lecture 3 - CSE@IIT Delhi
Lecture 3 - CSE@IIT Delhi

Mathematical Reasoning (Part III)
Mathematical Reasoning (Part III)

HOARE`S LOGIC AND PEANO`S ARITHMETIC
HOARE`S LOGIC AND PEANO`S ARITHMETIC

MMConceptualComputationalRemainder
MMConceptualComputationalRemainder

Gresham Ideas - Gresham College
Gresham Ideas - Gresham College

Hilbert Type Deductive System for Sentential Logic, Completeness
Hilbert Type Deductive System for Sentential Logic, Completeness

Logic and Proofs1 1 Overview. 2 Sentential Connectives.
Logic and Proofs1 1 Overview. 2 Sentential Connectives.

HW 12
HW 12

Section 3.1: Direct Proof and Counterexample 1
Section 3.1: Direct Proof and Counterexample 1

Arindama Singh`s "Cantor`s Little Theorem"
Arindama Singh`s "Cantor`s Little Theorem"

Slides
Slides

... A Turing machine is a mathematical model for computation It consists of a head, an infinitely long tape, a set of possible states, and an alphabet of characters that can be written on the tape A list of rules saying what it should write and should it move left or right given the current symbol and s ...
The Logic of Conditionals
The Logic of Conditionals

... So, once you see that Q is not a tautological consequence of P1,…,Pn, you can be sure that there is no way to FT-prove Q from P1,…,Pn. ...
Chapter 2 Notes Niven – RHS Fall 12-13
Chapter 2 Notes Niven – RHS Fall 12-13

Lec11Proofs05
Lec11Proofs05

Lec11Proofs
Lec11Proofs

Notes
Notes

Section 1.4 Mathematical Proofs
Section 1.4 Mathematical Proofs

Basics in Mathematical Logic 1 Assertions
Basics in Mathematical Logic 1 Assertions

Book Review: Lorenz J. Halbeisen: “Combinatorial Set Theory.”
Book Review: Lorenz J. Halbeisen: “Combinatorial Set Theory.”

1 Proof of set properties, concluded
1 Proof of set properties, concluded

< 1 ... 16 17 18 19 20 21 22 23 24 ... 27 >

Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem.The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an ""effective procedure"" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
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