The post "Ostroda Reggae Festival – Fotos 24.7.25" has just been published at https://www.irieites.de/?p=38833 #Bakshish #Banach #Spiety #TomaszMisztal

🌘 Banach–Tarski 悖論 - 維基百科
➤ Banach–Tarski 悖論的形式和相關研究
✤ https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Banach–Tarski 悖論是集合論幾何的定理，它聲稱在三維空間中，一個實心球可以分解成有限個不相交的子集，然後重新組合成兩個與原始球相同的球體。該悖論的形式也聲明瞭給定任何兩個“合理”的實際對象，它們的切割部分可以重新組合成對方。悖論依賴於座標集合論公理的選擇，並被認為違反了基本幾何直覺。
+ 這是一個令人驚訝的悖論，對幾何學有很大的挑戰。
+ 這個悖論實在太難以置信了，我無法想像怎麼可能。
#Banach–Tarski 悖論 #幾何定理 #悖論解析

Jedna z moich ulubionych krakowskich opowieści. Ta oraz o doktoracie Banacha :) Choć o doktoracie to już trzeba uogólnić - zatem jest to galicyjska opowieść ;)

#genialni #matematycy #rzeźba #pomnik #Banach #matematyka #krakow #Kraków #planty #ławka

** Old tweet**
every dependent D set d contains a finite D set I . linear D of arbitrary subsets of infinite-dimensional vector spaces (but not infinite d as in Hilbert, #Banach spaces), algebraic d in arbitrary subsets of field extensions of infinite transcendence degree

#Banach could divide 3d Ball st. using only rotations, translations he constructed two identical copies of the original Ball.
He got complete normed vector spaces names after him
Let me highlight this : ball NOT Rubik's cube
Tweet doesn't endorse drugs

- every dependent set d contains a finite dependent set I . linear dependence of arbitrary subsets of infinite-dimensional vector spaces (but not infinite d as in Hilbert, #Banach spaces), algebraic d in arbitrary subsets of field extensions of infinite transcendence degree

- #Banach's fixed-point theorem is also applied in proving the existence of solutions of ordinary differential equations, and is used in one proof of the inverse function theorem