Related papers: The Erdos Paradox
The article presents the detailed analysis of the watch paradox. It is shown that it arose because of unjustified, as it turned out, identification of watch readings at the moment of its return with the time read by it.
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
In 1930s Paul Erdos conjectured that for any positive integer C in any infinite +1 -1 sequence (x_n) there exists a subsequence x_d, x_{2d}, ... , x_{kd} for some positive integers k and d, such that |x_d + x_{2d} + ... + x_{kd}|> C. The…
This is a survey on Sarnak's Conjecture
This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. The historical…
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
This is a survey of some of Erd\H os's work on bases in additive number theory.
The implications of the original misunderstanding of the etymology of the word "ergodic" are discussed, and the contents of a not too well known paper by Boltzmann are critically examined. The connection with the modern theory of Ruelle is…
The "paradox" arises in the Two Envelopes Paradox from the incorrect formulation of the argument. The infomation given is misused and therefore the results are incorrect for the question asked. The key is to be clear on what question we are…
The story on the early days of the Quantum Ergodic Theorem. Alternative proof, underlying heuristics, physical analogies and interpretations.
In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically,…
We discuss the significance of some interesting results by Barbara Rokowska about combinatorial constructions. Her interest in finite mathematics and number theory began with an embellishment and detailing of some work by Erdos. Rokowska…
The Sorites paradox is the name of a class of paradoxes that arise when vague predicates are considered. Vague predicates lack sharp boundaries in extension and is therefore not clear exactly when such predicates apply. Several approaches…
In this article, we establish an additive decomposition of the discrete zeta function (for $s \in \mathbb{N}^*$, $s > 1$), more precisely of the function $4(\zeta(s)-1)$, as a series whose general term is of the form $1/x_n(s) + 1/y_n(s) +…
This is a survey article in algebraic logic, where we take a magical tour from old concepts due to Henkin, Monk and Tarski like neat embeddings, to modern views and perspectives, culminating in the use of Erdos graphs in settling important…
In 1930s Paul Erdos conjectured that for any positive integer $C$ in any infinite $\pm 1$ sequence $(x_n)$ there exists a subsequence $x_d, x_{2d}, x_{3d},\dots, x_{kd}$, for some positive integers $k$ and $d$, such that $\mid \sum_{i=1}^k…
The problem of absolute motion in the context of the twin paradox is discussed. It is shown that the various versions of the clock paradox feature some aspects which Mach might have been appreciated. However, the ultimate cause of the…
A model is constructed and a paradox concerning the proper direction and magnitude of the external force to maintain the equilibrium state of a parallel plate capacitor system is raised. By a thorough study of the model using different…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…