Resolving the Infinitude Controversy

From Euclid to Present: A Collection of Proofs regarding the Infinitude of Primes

Prime numbers are considered the basic building blocks of the counting numbers, and thus a natural question is: Are there infinitely many primes? Around 300BC, Euclid demonstrated, with a proof by contradiction, that infinitely many prime numbers exist. Since his work, the development of various fields of mathematics has produced subsequent proofs of the infinitude of primes. Each new and uniqu...

Prime Numbers in Certain Arithmetic Progressions

We discuss to what extent Euclid’s elementary proof of the infinitude of primes can be modified so as to show infinitude of primes in arithmetic progressions (Dirichlet’s theorem). Murty had shown earlier that such proofs can exist if and only if the residue class (mod k ) has order 1 or 2. After reviewing this work, we consider generalizations of this question to algebraic number fields.

‘An Infinitude of Possible Worlds’: Towards a Research Method for Hypertext Fiction

On the non-triviality of the basic Iwasawa λ-invariant for an infinitude of imaginary quadratic fields

Towards a proof of the decidability of the momentary stagnation of the growth function of D0L systems

This paper proves the decidability of several problems in the theory of HD0L, D0L and PD0L systems, some of which that have been proved before but are now proved in a different way. First, the paper tackles the decidability of the nilpotency of HD0L systems and the infinitude of PD0L languages. Then, we prove the decidability of the problem of momentary stagnation of the growth function of PD0L...