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...