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.
Ordered field
Strowski determinant
Axiom constant
Archimedes constant
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Index structure
Strowski Structure
Algebraic structure
Rational number structures
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Holms
Otto Stolz
Ostrowski
Archimedes
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Strowski theorem
Archimedean
Non-Archimedean
Heron's theorem
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Cinematography
Local field
Mechanics
Medicine
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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
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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
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Irrational function
Rational function
Real number function
Strowski constant
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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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