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UID:9127@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20251127T170000
DTEND;TZID=Europe/Paris:20251127T180000
DTSTAMP:20260625T132025Z
URL:https://www.i2m.univ-amu.fr/evenements/all-human-beings-are-born-free-
 and-equal-but-not-numbers/
SUMMARY:Adrien Mounier (I2M): "All human beings are born free and equal..."
  but not numbers
DESCRIPTION:Adrien Mounier: Abstract: This is the story of a date between 
 two real numbers\, Alpha and Phi. Alpha introduces themselves succinctl
 y\, and within two minutes they have already laid out an almost complete p
 icture of their personality. As a good rational number\, Alpha try to get 
 to know their mysterious interlocutor a little better:\n\n"So\, are you mo
 re rational or irrational?"\n\n\nPhi\, faced with this rather odd question
 \, frowns slightly and replies:\n\n\n"I find your way of seeing things ver
 y binary. It's a bit reductive to place people into only two categories wh
 en numbers are so diverse!"\n\n\nAlpha then feels a bit silly and\, in a s
 lightly embarrassed tone\, continues:\n\n\n"Alright\, I see—but you have
  to be one of the two\, because if you're not one\, then you're the other!
 "\n\n\nPhi rolls their eyes and retorts:\n\n\n"Has it never occurred to yo
 u that some of us are more irrational than others? I even have friends who
  don't let themselves be easily approached by simple rational numbers! As 
 for me\, I am the most irrational of all irrational creatures—and I can 
 prove it!"\n\n\nAnd so Phi plunged Alpha into the wonderful adventure of 
 Diophantine approximation. Until then\, Alpha had been used to approaching
  irrationals in a direct way\, by spelling out their decimal expansions—
 but it must be admitted that irrationals quickly grew tired of that unorig
 inal approach. Phi\, however\, was more subtle: by using continued fracti
 ons\, they showed Alpha a far more efficient way to approach irrational nu
 mbers (which greatly piqued Alpha's interest). Finally\, Phi showed that t
 here exists a measure of irrationality that makes it possible to classif
 y irrational numbers—and even that some of them have an infinite measur
 e of irrationality!
CATEGORIES:Séminaire,Rencontres doctorant⋅es I2M-CPT
LOCATION:Luminy - salle 500-504b\, Aix-marseille université-faculté des s
 ciences\, campus Luminy\, Marseille\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Aix-marseille université-f
 aculté des sciences\, campus Luminy\, Marseille\, France;X-APPLE-RADIUS=1
 00;X-TITLE=Luminy - salle 500-504b:geo:0,0
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