Content deleted Content added
Tom.Reding (talk | contribs) m +{{Authority control}} (3 IDs from Wikidata); WP:GenFixes & cleanup on |
Reverting edit(s) by 2603:7000:7700:4BE3:5E74:9912:8C1E:8CD2 (talk) to rev. 1201422669 by JoaoFrancisco1812: Non-constructive edit (UV 0.1.5) |
||
(3 intermediate revisions by 3 users not shown) | |||
Line 18:
}}</ref>
By contrast, the [[Brouwer fixed-point theorem]] (1911) is a non-[[Constructivism (mathematics)|constructive result]]: it says that any [[continuous function]] from the closed [[unit ball]] in ''n''-dimensional [[Euclidean space]] to itself must have a fixed point,<ref>Eberhard Zeidler, ''Applied Functional Analysis: main principles and their applications'', Springer, 1995.</ref> but it doesn't describe how to find the fixed point (
For example, the [[cosine]] function is continuous in [−1, 1] and maps it into [−1,
The [[Lefschetz fixed-point theorem]]<ref>{{cite journal |author=Solomon Lefschetz |title=On the fixed point formula |journal=[[Annals of Mathematics|Ann. of Math.]] |year=1937 |volume=38 |pages=819–822 |doi=10.2307/1968838 |issue=4}}</ref> (and the [[Nielsen theory|Nielsen fixed-point theorem]])<ref>{{cite book
Line 86:
*[[Caristi fixed-point theorem]]
*[[Diagonal lemma]], also known as the fixed-point lemma, for producing self-referential sentences of [[first-order logic]]
*[[Lawvere's fixed-point theorem]]
*[[Discrete fixed-point theorem]]s
*[[Earle-Hamilton fixed-point theorem]]
|