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Definition: Order Relation for Natural Numbers

Let \(x,y\in\mathbb N\) be any given natural numbers. The relations “\( > \)” greater, “\( < \)” smaller and “\( = \)” equal have been defined already from the set-theoretic point of view. These relations can be explained more intuitively by the comparison of natural numbers using the concept of addition explains:

We call the numbers

Moreover, we say

Obviously, by this definition

| | | | | created: 2014-06-21 14:18:26 | modified: 2020-06-25 10:07:30 | by: bookofproofs | references: [696]

1.Proposition: Transitivity of the Order Relation of Natural Numbers

2.Proposition: Addition of Natural Numbers Is Cancellative With Respect To Inequalities

3.Proposition: Order Relation for Natural Numbers, Revised

4.Proposition: Every Natural Number Is Greater or Equal Zero

5.Proposition: Multiplication of Natural Numbers Is Cancellative With Respect to the Order Relation

6.Proposition: Comparing Natural Numbers Using the Concept of Addition

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[696] Kramer Jürg, von Pippich, Anna-Maria: “Von den natürlichen Zahlen zu den Quaternionen”, Springer-Spektrum, 2013