Archimedean Principle

Posted on February 13, 2017 by Sumant Sumant

Archimedean Property

There are 4 equivalent ways to express Archimedean Principle
1. If a,b \in \mathbb{R^+} then there exists an n \in \mathbb{N} such that na > b.
2. The set of Positive Integers (Natural Numbers) is unbounded. For all natural numbers n \in \mathbb{N}, \exists
3. If x \in \mathbb{R} then there exists an n \in \mathbb{N} such that n \le x < n+1.
4. If x \in \mathbb{R} then there exists an n \in \mathbb{N} such that \frac{1}{n} < x.

About Sumant Sumant

I love Math and I am always looking forward to collaborate with fellow learners. If you need help learning math then please do contact me.
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