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Mathematical exceptions to the rules or intuitionSun, 20 Aug 2017 17:11:55 +0000hourly1https://wordpress.org/?v=4.8.1Comment on A function continuous at all irrationals and discontinuous at all rationals by A semi-continuous function with a dense set of points of discontinuity | Math Counterexamples
http://www.mathcounterexamples.net/a-function-continuous-at-all-irrationals-and-discontinuous-at-all-rationals/#comment-10223
Sun, 20 Aug 2017 17:11:55 +0000http://www.mathcounterexamples.net/?p=694#comment-10223[…] proved here that (f) right-sided and left-sided limits vanish at all points. Therefore (limsuplimits_{x […]
]]>Comment on Counterexamples around series (part 1) by Counterexamples around series (part 2) | Math Counterexamples
http://www.mathcounterexamples.net/counterexamples-around-series-part-1/#comment-10215
Sun, 09 Jul 2017 14:49:17 +0000http://www.mathcounterexamples.net/?p=1363#comment-10215[…] follow the article counterexamples around series (part 1) providing additional funny series […]
]]>Comment on Counterexamples around cardinality (part 2) by An uncountable chain of subsets of the natural numbers | Math Counterexamples
http://www.mathcounterexamples.net/counterexamples-around-cardinality-part2/#comment-10214
Sun, 28 May 2017 14:33:06 +0000http://www.mathcounterexamples.net/?p=984#comment-10214[…] Let’s first recall that the set of the rational numbers (mathbb Q) is countable. Hence one can find a bijection (varphi : mathbb Q to mathbb N) (see following article). […]
]]>Comment on Counterexamples on real sequences (part 2) by Counterexamples on real sequences (part 3) | Math Counterexamples
http://www.mathcounterexamples.net/counterexamples-on-real-sequences-part-2/#comment-10213
Sun, 21 May 2017 20:22:16 +0000http://www.mathcounterexamples.net/?p=561#comment-10213[…] This article is a follow-up of Counterexamples on real sequences (part 2). […]
]]>Comment on Cantor set: a null set having the cardinality of the continuum by A strictly increasing continuous function that is differentiable at no point of a null set | Math Counterexamples
http://www.mathcounterexamples.net/cantor-set_a-null-set-having-the-power-of-the-continuum/#comment-10212
Mon, 08 May 2017 15:25:08 +0000http://www.mathcounterexamples.net/?p=364#comment-10212[…] We build in this article a strictly increasing continuous function (f) that is differentiable at no point of a null set (E). The null set (E) can be chosen arbitrarily. In particular it can have the cardinality of the continuum like the Cantor null set. […]
]]>Comment on Existence of a continuous function with divergent Fourier series by Post formatting bug in WordPress * Best Wordpress Themes - Reviews
http://www.mathcounterexamples.net/existence-continuous-function-with-divergent-fourier-series/#comment-10203
Sun, 05 Feb 2017 18:40:29 +0000http://www.mathcounterexamples.net/?p=1206#comment-10203[…] have a Math counterexamples blog. One post contains the […]
]]>Comment on A discontinuous additive map by A discontinuous midpoint convex function | Math Counterexamples
http://www.mathcounterexamples.net/a-discontinuous-additive-map/#comment-10201
Sun, 20 Nov 2016 09:49:38 +0000http://www.mathcounterexamples.net/?p=1211#comment-10201[…] to my previous article on the existence of discontinuous additive map, let’s use a Hamel basis (mathcal B = (b_i)_{i in I}) of (mathbb R) considered as a […]
]]>Comment on Differentiability of multivariable real functions (part1) by Differentiability of multivariable functions | Physics Forums - The Fusion of Science and Community
http://www.mathcounterexamples.net/differentiability-multivariable-real-functions-part1/#comment-10192
Mon, 31 Oct 2016 17:32:16 +0000http://www.mathcounterexamples.net/?p=824#comment-10192[…] function having directional derivatives along all directions which is not differentiable" at http://www.mathcounterexamples.net/differentiability-multivariable-real-functions-part1/ Stephen Tashi, Oct 31, 2016 at 12:32 […]
]]>Comment on A continuous function with divergent Fourier series by Existence of a continuous function with divergent Fourier series | Math Counterexamples
http://www.mathcounterexamples.net/continuous-function-with-divergent-fourier-series/#comment-10190
Sat, 29 Oct 2016 13:12:39 +0000http://www.mathcounterexamples.net/?p=1085#comment-10190[…] that article, I provided an example of a continuous function with divergent Fourier series. We prove here the […]
]]>Comment on Continuity of multivariable real functions by Continuity of ##g(x,y)## and its partials | Physics Forums - The Fusion of Science and Community
http://www.mathcounterexamples.net/continuity-multivariable-real-functions/#comment-10185
Mon, 10 Oct 2016 16:56:04 +0000http://www.mathcounterexamples.net/?p=803#comment-10185[…] However, there are examples where that result is not sufficient to prove continuity. This page http://www.mathcounterexamples.net/continuity-multivariable-real-functions/ has an example of a function ##g(x,y)## where the limit along any line through the origin exists […]
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