Editing Feigenbaum constants (section)

==Properties==
Both numbers are believed to be [[transcendental number|transcendental]], although they have not been [[mathematical proof|proven]] to be so.<ref>{{Cite thesis |last=Briggs |first=Keith |title=Feigenbaum scaling in discrete dynamical systems |degree=PhD |publisher=[[University of Melbourne]] |url=http://keithbriggs.info/documents/Keith_Briggs_PhD.pdf |year=1997}}</ref> In fact, there is no known proof that either constant is even [[irrational number|irrational]].

The first proof of the [[universality (dynamical systems)|universality]] of the Feigenbaum constants was carried out by [[Oscar Lanford]]—with computer-assistance—in 1982<ref>{{cite journal |last=Lanford III |first=Oscar |year=1982 |title=A computer-assisted proof of the Feigenbaum conjectures |journal=Bull. Amer. Math. Soc. |volume=6 |issue=3 |pages=427–434 |doi=10.1090/S0273-0979-1982-15008-X |doi-access=free}}</ref> (with a small correction by [[Jean-Pierre Eckmann]] and Peter Wittwer of the [[University of Geneva]] in 1987<ref>{{Cite journal |last1=Eckmann |first1=J. P. |last2=Wittwer |first2=P. |year=1987 |title=A complete proof of the Feigenbaum conjectures |journal=Journal of Statistical Physics |volume=46 |issue=3–4 |pages=455 |bibcode=1987JSP....46..455E |doi=10.1007/BF01013368 |s2cid=121353606}}
</ref>).  Over the years, non-numerical methods were discovered for different parts of the proof, aiding [[Mikhail Lyubich]] in producing the first complete non-numerical proof.<ref>{{cite journal |last=Lyubich |first=Mikhail |year=1999 |title=Feigenbaum-Coullet-Tresser universality and Milnor's Hairiness Conjecture |journal=Annals of Mathematics |volume=149 |issue=2 |pages=319–420 |arxiv=math/9903201 |bibcode=1999math......3201L |doi=10.2307/120968 |jstor=120968 |s2cid=119594350}}</ref>