Axiom Archimedes or Archimedean property is the property of having no infinitely or infinitely small elements. It was derived from the work of Archimedes, known as the Axiom V of Archimedes, on Spheres and Cylinders. Try to ace this quiz.
It contains irrational number
If x is infinitesimal its inverse is also infinite
It contains rational number
If x is infinitesimal and r is rational their products are also infinite
Let x be any element of K. Then there exists a rational number r such that r > x
Let x be any element of K. Then there exists a natural number n such that n = x
Let x be any element of K. Then there exists a natural number n such that n < x
Let x be any element of K. Then there exists a natural number n such that n > x
Rational number structures
Real number function
The natural numbers are cofinal in K
For any x in K the set of integers greater than x has a least element
Zero is the infimum of a set
Every nonempty open interval of K contains a natural number
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