Numbers and Infinities
By Tom Brown
"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
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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...
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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...
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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...
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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...
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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
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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...
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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...
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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...
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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...
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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...
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Statics and Relativity
Classical Mechanics is divided into two disciplines: Statics is where a structure or system of particles remains fixed, whereas dynamics involves...
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Some theorems on sets
This view of the infinite, which I consider to be the sole correct one, is held by only a few. I entertain no doubts as to the truths of the...
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Elementary set theory
Georg Cantor (1845 – 1918) The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent...
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The Travelling Salesman and Chess
To do routing, timetables and scheduling, if you wonder how good artificial intelligence is give it the travelling salesman problem. Then we'll see...
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The Travelling Salesman Game
The Travelling Salesman Problem can be represented by a graph, to start with as one specific simply formulated problem hopefully then generalised...
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The Travelling Salesman Mathematics
Addition : Examples If you are familiar with these ideas you could skip it to the part on algorithms. Don't worry this essay is the only mathematics...
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Is a given number divisible?
There are some very simple tests to find a given integer divisible, for instance 180 is divisible by 4, or 21 by 3. We probably did the tests in...
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Scientific accuracy and discrepancies
Can someone tell us what the correct use is of the terms figures, numbers, amount of, count and how many? These terms have different meanings. The...
Consistency in Lists of Numbers
A measure of probability distribution for consistency in large lists of numbers is explained. If there are discrepancies it would be a sign of...
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