Numbers and Infinities

"Most of the fundamental ideas of science are essentially simple, and may,
as a rule, be expressed in a language comprehensible to everyone."

Albert Einstein and Leopold Infeld

The concept Zero

The very simple concept of Zero (“null” or “naught” or “nothing”) as in effect a number, contributed greatly to a dramatic development of modern...
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The Nature of Numbers

For interest's sake we discuss different types of numbers: ordinals, cardinals as well as measures, and just names. The first is a count in order as...

Naïve set theory

The cardinality of a set would give how many elements it has. An "infinite set" can be characterised as a set being equivalent to a strict subset of...

Mathematical Induction

Induction is a method of proving certain theorems. The idea is a bit sophisticated but in essence it is simple. In the following the reasoning is...

Infinite Series

The essay is meant for people with some after-school mathematics training and just to understand some theory it is not meant as rigorous at all just...

A little challenge

A problem from my post of Infinite Series, find the sum as just a simple formula (a rational function) of: 1 + 1/4 + 1/9 + 1/16 + ... + 1/n²

An Exercise in Relativity

Consider the following situation: Imagine a relativistic mathematical model where a train is heading straight to the station at a speed u, distance...

What is the Age of the Universe?

What is the Age of the Universe? Is there such a thing? No, there is not. What would it mean? If I want to establish “The age” it would obviously...

The Railway Problem

When doing a post-graduate Topology course I asked another student for advice, “I don't understand this what does it say?” that was a seemingly...

Measuring Temperature

What is the definition of Temperature? How is it measured? What is the temperature of a vacuum? Does it make sense? - At other extremes plasma, such...

How many Universes are there?

As far as I am concerned there is Only One Universe. This is in fact what the word means it doesn't make sense for there to be more. Actually we must...