What is an integer ? A crafty representation
Integers are an extension of the natural numbers where the existence of subtraction provides a more appropriate framework for certain questions of arithmetic. They can be described axiomatically, but can
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What is a natural number? Defining or axiomatising
Mathematical science does not seek to define the notion of a natural number, but to understand the set of natural numbers.
"Natural numbers have been made by God, everything else is
An infinity of prime numbers : Euclid’s theorem
The prime natural numbers are those which have no divisors other than 1 and themselves. They exist in infinite number by Euclid's theorem, which is not difficult to prove.
1.Prime numbers
1.1.Divisors
Finiteness and Mathematical Infinity : Comparing and Enumerating
A finite set is a set that can be counted using the natural numbers \(1,\ldots,n\) for a certain natural number \(n\). But what is counting ? And then, what is
What is a set? Founding mathematics in intuition
Naive set theory or "potato science" is the natural (and understandable!) foundation of mathematical science.
"I know what time is. If you ask me, I don't know anymore." Augustine.
This insightful quote