In nonstandard analysis, a discipline within classical mathematics, microcontinuity (or S-continuity) of an internal function f at a point a is defined...
4 KB (600 words) - 03:33, 3 December 2024
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
107 KB (10,831 words) - 22:10, 16 June 2025
≈ 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...
25 KB (3,981 words) - 00:52, 10 February 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
22 KB (2,376 words) - 19:34, 18 June 2025
continuity closely parallels the infinitesimal definition used today (see microcontinuity). The formal definition and the distinction between pointwise continuity...
63 KB (9,309 words) - 11:22, 27 May 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
76 KB (8,805 words) - 06:25, 7 June 2025
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...
3 KB (401 words) - 06:49, 18 February 2020
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
84 KB (11,658 words) - 04:06, 8 June 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
24 KB (3,099 words) - 02:27, 2 May 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
42 KB (5,401 words) - 01:53, 9 June 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
33 KB (4,924 words) - 01:41, 9 June 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
37 KB (5,092 words) - 16:24, 23 May 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
155 KB (19,219 words) - 23:45, 15 June 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
31 KB (3,978 words) - 00:54, 22 April 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
15 KB (2,415 words) - 15:04, 3 April 2025
f_{n}^{*}(x)} is infinitely close to f ∗ ( x ) {\displaystyle f^{*}(x)} (see microcontinuity for a similar definition of uniform continuity). In contrast, pointwise...
30 KB (5,341 words) - 21:39, 6 May 2025
{st} \circ f} is constant on the halo of x {\displaystyle x} . See microcontinuity for more details. Adequality Nonstandard calculus Katz, Karin Usadi;...
7 KB (1,079 words) - 03:30, 3 December 2024
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
27 KB (3,994 words) - 18:39, 27 May 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
19 KB (2,780 words) - 10:15, 17 April 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
9 KB (593 words) - 15:22, 12 January 2025
cannot be realized in full. Bŀaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize...
69 KB (11,342 words) - 05:33, 6 June 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
17 KB (2,826 words) - 20:41, 9 June 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
4 KB (438 words) - 11:27, 21 February 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
15 KB (1,966 words) - 13:34, 1 May 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
9 KB (756 words) - 01:22, 11 May 2025
not be realized in full. Błaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize...
13 KB (1,370 words) - 19:27, 16 June 2025
function - an analogue of a continuous function in discrete spaces. Microcontinuity – Mathematical term Normal function – Function of ordinals in mathematics...
25 KB (3,769 words) - 16:00, 31 May 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
36 KB (6,834 words) - 16:34, 6 March 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
4 KB (331 words) - 09:31, 4 April 2025
set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity Mathematicians Gottfried Wilhelm...
7 KB (971 words) - 05:09, 28 April 2025