Thanks to the Axiom V of Archimedes’ On the Sphere and Cylinder, the axiom of Archimedes (or Archimedean axiom, Archimedes' axiom, Archimedes' lemma, or the continuity axiom) is one of the most widespread concepts in mathematical analysis and the field of abstract algebra.
It states that one magnitude can find a multiple of either of two magnitudes which will exceed the other, given the magnitudes have a ratio.
Infinitely small
Large
Equal
Small
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Field of the trigonometric functions
Field of real numbers
Field of integers
Field of rational functions
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1870s
1880s
1890s
1900s
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Non-Archimedean
Archimedean
Linear-Archimedean
Algebraic-Archimedean
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Otto Stolz
Reynald Harvey
Paul Autz
Charles Puma
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Non-Archimedean
Archimedean
Linear-Archimedean
Algebraic-Archimedean
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Global field
Exponential functions
Local field
Trigonometric functions
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Positive elements
Negative elements
Integers
Real numbers
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Field of the trigonometric functions
Field of real numbers
Field of integers
Field of rational functions
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