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{"slip": { "id": 220, "advice": "Most things are not as bad as you think they are."}}

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{"type":"standard","title":"Uniform convergence","displaytitle":"Uniform convergence","namespace":{"id":0,"text":""},"wikibase_item":"Q1411887","titles":{"canonical":"Uniform_convergence","normalized":"Uniform convergence","display":"Uniform convergence"},"pageid":50652,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Uniform_convergence.svg/330px-Uniform_convergence.svg.png","width":320,"height":270},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Uniform_convergence.svg/640px-Uniform_convergence.svg.png","width":640,"height":540},"lang":"en","dir":"ltr","revision":"1289165889","tid":"93317b0e-2ac2-11f0-a7c4-f2ce92673bf7","timestamp":"2025-05-06T21:39:23Z","description":"Mode of convergence of a function sequence","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Uniform_convergence","revisions":"https://en.wikipedia.org/wiki/Uniform_convergence?action=history","edit":"https://en.wikipedia.org/wiki/Uniform_convergence?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Uniform_convergence"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Uniform_convergence","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Uniform_convergence","edit":"https://en.m.wikipedia.org/wiki/Uniform_convergence?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Uniform_convergence"}},"extract":"In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in . Described in an informal way, if converges to uniformly, then how quickly the functions approach is \"uniform\" throughout in the following sense: in order to guarantee that differs from by less than a chosen distance , we only need to make sure that is larger than or equal to a certain , which we can find without knowing the value of in advance. In other words, there exists a number that could depend on but is independent of , such that choosing will ensure that for all . In contrast, pointwise convergence of to merely guarantees that for any given in advance, we can find such that, for that particular , falls within of whenever .","extract_html":"

In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions $\text{[math]}$ converges uniformly to a limiting function $\text{[math]}$ on a set $\text{[math]}$ as the function domain if, given any arbitrarily small positive number $Poprzednia Następna$