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.
Otto Stolz
Reynald Harvey
Paul Autz
Charles Puma
Linear structure
Algebraic structure
Trigonometric structure
Exponential structure
Infinitely small
Large
Equal
Small
Non-Archimedean
Archimedean
Linear-Archimedean
Algebraic-Archimedean
Non-Archimedean
Archimedean
Linear-Archimedean
Algebraic-Archimedean
Global field
Exponential functions
Local field
Trigonometric functions
Field of the trigonometric functions
Field of real numbers
Field of integers
Field of rational functions
Field of the trigonometric functions
Field of real numbers
Field of integers
Field of rational functions
1870s
1880s
1890s
1900s
Positive elements
Negative elements
Integers
Real numbers