MERLOT Materials

The two axioms which define intuitive set theory, Axiom of Combinatorial Sets and Axiom of Infinitesimals, are stated.... see more

Axiom of Combinatorial Sets is defined and used to derive Generalized Continuum Hypothesis.

Generalized Pythagoras theorem is discussed in terms of matrices.

Logset, the inverse of the powerset operation, is introduced into set theory.

Generalized Continuum Hypothesis is derived from a simple axiom called Axiom of Combinatorial Sets.

Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to... see more

Twenty significant and pressing problems of information technology are listed.

A weblog in which the use of multimedia in distance education is discussed.

NuMachine, as powerful as Turing machine, but more intuitive in its working is described. Adding three more derivation... see more

Intellectual space is defined as the set of all proofs of mathematical logic, contained in The Book of Erdos. Physical... see more

Engineers know that they can land a man on the moon without using the Lebesgue integral and they will never encounter... see more

Continuum Hypothesis is derived from an axiom called Axiom of Combinatorial Sets. The derivation is simple enough to be... see more

The biggest mystery for me is that the sequence of symbols we scribble on paper is able to simulate our complex universe.... see more

Riemann Hypothesis is viewed as a statement about the power dissipated in an electrical network.

Five geometrical eqivalents of Goldbach conjecture are given, calling one of them Fermat Like Theorem.

Riemann Hypothesis is viewed as a statement about the capacity of a communication channel as defined by Shannon.

A weblog in which issues of metamathematics are discussed.

An axiomatic theory called Real Set Theory is defined in which Generalized Continuum Hypothesis and Axiom of Choice are... see more

Godel has proved that there are formulas in Elementary Arithmetic, which will introduce contradictions, irrespective of... see more

A complete analysis of Shannon's telegraph channel is given, making use of matrices with elements from a division ring. A... see more

The most popular format for publishing mathematics on the Web is the PDF, and HyperLaTeX is the program which allows us... see more

The mathematical universe discussed here gives models of possible structures our physical universe can have.

The mathematical universe discussed here gives models of possible structures our physical universe can have.

It is not unusual that instructors get bogged down in the complex details of set theory, while teaching the foundations... see more