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Mathematical term
In nonstandard analysis, a discipline within classical mathematics, microcontinuity (or S-continuity) of an internal function f at a point a is defined
Microcontinuity
Swiss mathematician (1707–1783)
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Leonhard_Euler
Modern application of infinitesimals
≈ f ∗ ( y ) {\displaystyle f^{*}(x)\approx f^{*}(y)} . In terms of microcontinuity defined in the previous section, this can be stated as follows: a real
Nonstandard_calculus
French mathematician and lawyer (1601–1665)
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Pierre_de_Fermat
Branch of mathematics
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Calculus
Mathematical treatise by Archimedes
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
The Method of Mechanical Theorems
The_Method_of_Mechanical_Theorems
Generalization of the real numbers
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Surreal_number
1976 mathematics textbook by H. Jerome Keisler
not be realized in full. Błaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize
Elementary Calculus: An Infinitesimal Approach
Elementary_Calculus:_An_Infinitesimal_Approach
Mathematical symbol used to denote integrals and antiderivatives
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Integral_symbol
Extremely small quantity in calculus; thing so small that there is no way to measure it
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Infinitesimal
Real numbers adjoined with a nil-squaring element
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Dual_number
Type of internal set in nonstandard analysis
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Hyperfinite_set
Mathematical function with no sudden changes
continuity closely parallels the infinitesimal definition used today (see microcontinuity). The formal definitions for, and distinction between, pointwise continuity
Continuous_function
Function from the limited hyperreal to the real numbers
{st} \circ f} is constant on the halo of x {\displaystyle x} . See microcontinuity for more details. Adequality Nonstandard calculus Katz, Karin Usadi;
Standard_part_function
German polymath (1646–1716)
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Gottfried_Wilhelm_Leibniz
Mathematical notion of infinitesimal difference
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Differential_(mathematics)
French mathematician (1789–1857)
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Augustin-Louis_Cauchy
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Hyperreal_number
Mathematical notation used for calculus
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Leibniz's_notation
System of mathematical set theory
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Internal_set_theory
Calculus using a logically rigorous notion of infinitesimal numbers
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Nonstandard_analysis
Mode of convergence of a function sequence
{f}_{n}^{*}(x)} is infinitely close to f ∗ ( x ) {\displaystyle {f}^{*}(x)} (see microcontinuity for a similar definition of uniform continuity). In contrast, pointwise
Uniform_convergence
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Criticism of nonstandard analysis
Criticism_of_nonstandard_analysis
Point to which functions converge in analysis
cannot be realized in full. Bŀaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize
Limit_of_a_function
Calculus textbook by Guillaume de l'Hôpital (1696)
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Analyse des infiniment petits pour l'intelligence des lignes courbes
Analyse_des_infiniment_petits_pour_l'intelligence_des_lignes_courbes
American mathematician
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Abraham_Robinson
Mathematical procedure equivalent to differential calculus
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Adequality
Principle that whatever succeeds for the finite also succeeds for the infinite
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Law_of_continuity
Relation among continuous functions
function - an analogue of a continuous function in discrete spaces. Microcontinuity – Mathematical term Normal function – Function of ordinals in mathematics
Equicontinuity
Textbook by Augustin-Louis Cauchy (1821)
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Cours_d'analyse
System of numbers with non-finite quantities
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Levi-Civita_field
Named set of points in nonstandard analysis
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Monad_(nonstandard_analysis)
Geometrical concept relating area and volume
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Cavalieri's_principle
Proof technique in nonstandard analysis
express the property known in nonstandard analysis as S-continuity (or microcontinuity) of ƒ at x. S-continuity is referred to as an external property. The
Overspill
Type of set in mathematical logic
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Internal_set
Ordered field that does not satisfy the Archimedean property
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Non-Archimedean_ordered_field
Hyperreal number that is equal to its own integer part
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Hyperinteger
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Increment_theorem
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Constructive nonstandard analysis
Constructive_nonstandard_analysis
Formalization in mathematical topos theory
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Synthetic differential geometry
Synthetic_differential_geometry
Mathematical model for describing material deformation under stress
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Infinitesimal_strain_theory
Heuristic principle enunciated by Gottfried Wilhelm Leibniz
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Transcendental law of homogeneity
Transcendental_law_of_homogeneity
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Glossary_of_calculus
1734 book by George Berkeley
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
The_Analyst
Concept in model theory
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm
Transfer_principle
MICROCONTINUITY
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Male
Egyptian
, ("oath"); Bes.
Boy/Male
Muslim/Islamic
Servant of the Most Powerful
Girl/Female
Indian
Strong
Girl/Female
Indian
Maiden
Boy/Male
Gujarati, Hindu, Indian
Lord Krishna
Girl/Female
Australian, Finnish, German, Swedish, Teutonic
Peaceful Ruler; Peace-keeper; Female Version of Frederic; From the Old German Name Frithuric
Girl/Female
Australian
Blend of Rae (short form of Rachel: ewe) and the name element -ene.
Girl/Female
Latin
Mildness. The name Clementia was borne by the Roman goddess of mercy. Clementia and its variants...
Female
Hebrew
(ש×ָרï‹×Ÿ) Hebrew name SHAROWN means "plain, level ground." In the bible, this is the name of a valley in Palestine. The name is sometimes given because of its association with the flowering shrub called Rose of Sharon.Â
Boy/Male
Hindu
Close friend, Good company, Smart one, Companion, Supreme
MICROCONTINUITY
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MICROCONTINUITY