Related papers: How long is a Proof? - A short note
This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).
In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts…
This paper has been withdrawn by the author.
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.
This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…
Consider a short theorem, i.e. one that can be written down using just a few symbols. Can its shortest proof be arbitrarily long? We answer this question in the negative. Inspired by arguments by Calude et al (1999) and Chaitin (1984) that…
This paper as been withdrawn. This paper as been withdrawn. This paper as been withdrawn. This paper as been withdrawn. This paper as been withdrawn. This paper as been withdrawn.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
Withdrawn -- a revised version will appear in due course.
This paper has been withdrawn.
This paper has been withdrawn.
A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study the problem of checking whether a CNF formula (a set of clauses) is redundant, that is, it contains clauses that can be derived from the…
Only craziness I am ashamed about.
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
In this paper we present a short and elementary proof for the error in Simpson's rule.
Admin note: withdrawn by arXiv admin because of the use of a pseudonym, in violation of arXiv policy.
This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.