The Banach–Tarski Paradox
24:14
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Q: What's an anagram of Banach-Tarski?
A: Banach-Tarski Banach-Tarski.
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Infinity shapeshifter vs. Banach-Tarski paradox
14:58
Take on solid ball, cut it into a couple of pieces and rearrange those pieces back together into two solid balls of exactly the same size as the original ball. Impossible? Not in mathematics!
Recently Vsauce did a brilliant video on this so-called Banach-Tarski paradox:
In this prequel to the Vsauce video the Mathologer takes you on a whirlwind tour of mathematical infinities off the beaten track. At the end of it you'll be able to shapeshift any solid into any other solid. At the same time you'll be able to appreciate like a mathematician what's really amazing about the Banach-Tarski paradox.
Enjoy :)
This Math Theorem Proves that 1=1+1 | The Banach-Tarskis Paradox
33:27
Mathematicians are in nearly universal agreement that the strangest paradox in math is the Banach-Tarski paradox, in which you can split one ball into a finite number of pieces , then rearrange the pieces to get two balls of the same size. Interestingly, only a minority of mathematicians has ever seen the proof of this theorem. Rarely discussed, also, are the implications of this theorem, including that you can take a pea-sized ball, split it up into a finite number of pieces, and reassemble them into a ball the size of the Sun!
Presented by David Kung
Learn more about math paradoxes at
0:00 What Is the Banach-Tarski Paradox?
0:30 What Are the Implications of the Banach-Tarski Paradox?
2:00 A Word Version of the Banach-Tarski Paradox
04:00 Simplify by Removing Copies of Extra Letters
04:45 What Is Concatenation?
05:19 Every Word Has An Anti-word
05:50 Each Word Is a Complicated Series of Rotations
06:30 Visualize the A's Like a Triangle
06:50 Visualize the B's As Pairs
07:50 What Is a Cayley Diagram?
12:15 How to Visualize the Colors in the Diagram as Circles
14:30 Similarities with Infinity and Counting Numbers
15:30 Banach-Tarski Goal as Pertains to Rotations
18:57 How the Banach-Tarski Paradox Relates to Magic Tricks: Quick Conundrum
20:39 Felix Hausdorff Proved the Decomposition of G
21:40 A Sequence of Rotations Equals Another Single Rotation
23:34 Creating Equivalence Classes
24:30 Axiom of Choice
29:00 Two Additional Complications for the Banach-Tarski Paradox
30:35 Why the Set S is Unmeasurable
32:00 Any Bounded Set With Non-Empty Interior Can Make Any Other Such Set
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The Infinite Money Paradox
10:32
Deciding whether to play a game is usually very easy… you crunch the numbers and if they work in your favor, you play. If they don’t, you shouldn’t. Mathematical case closed.
But what happens when the math of a game tells you that you have access to infinite wealth and unlimited expected value and real life tells you not to play? Enter: The St. Petersburg Paradox.
The Bernoulli family first started corresponding about the paradox in the early 1700s with a series of letters examining the puzzling math behind the simple game. But it wasn’t until 1738 when Daniel Bernoulli realized that he could factor real life utility -- how much something actually means to you -- into the calculations.
The St. Petersburg Paradox opens up doors to how we think about what math really means to us, including modern research into Prospect Theory and everyday issues like whether we decide to buy life insurance. And in the end, one thing we know for sure: we’re all much, much more than numbers.
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The Banach-Tarski Paradox - Tales of the Forest
45:58
Hello everyone reading this description! Most of you that are already familiar with my channel know that I mainly post videos pertaining to genealogy (it's literally in my name), but I am also very interested in the subject of music.
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This is my first (and hopefully not last!) attempt at a studio album. Also I chose the name The Banach-Tarski Paradox.
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Infinite Chocolate Bar Trick
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banach tarski paradox
2:45
How the Axiom of Choice Gives Sizeless Sets | Infinite Series
13:20
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Does every set - or collection of numbers - have a size: a length or a width? In other words, is it possible for a set to be sizeless? This in an updated version of our September 8th video. We found an error in our previous video and corrected it within this version.
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The Infinite Hotel Paradox - Jeff Dekofsky
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The Banach Tarski paradox - is it nonsense? | Sociology and Pure Mathematics | N J Wildberger
17:08
One of the famous paradoxes of 20th century pure mathematics is the assertion that it is possible to subdivide a solid ball of radius 1 in three dimensional space into 5 disjoint pieces, take those five pieces and subject them to rigid motions, that is rotations and translations, to obtain the subdivision of a solid ball of radius 2. If it sounds crazy, no problem, we can't let reality intrude into the dreamings of us pure mathematicians. Even if our theories end up disconnected from reality and from common sense.
Is it time that we stopped paying lip service to logical nonsense -- even if it is supported by all kinds of axiomatics - in this case the modern pure mathematician's favourite: the Axiom of Choice?
Here is the blog from which the first part of the video is read: you can check out quite a few more math related discussions:
The Banach-Tarski Paradox
3:01
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Animation of the strangest paradox in math - the Banach-Tarski Paradox
25
from Mindbending Math: Paradoxes & Puzzles, from The Great Courses
Doubling Sphere Paradox - Banach-Tarski Theorem
1:19
Ever wonder how you can make two spheres out of one?
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This video was made in association with The Math Centre at Humber College, by Zack Barnes and Cheryl Yang.
Banach Tarski Paradox Crash Course
20:35
This is my final presentation for my Math Seminar Class (MATH 410) at Chadron State College.
The Banach-Tarski Paradox
1:01
Sezione video del Concorso Martemartiamo
The Banach-Tarski Paradox
2:03
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Measure theory: Why measure theory - The Banach-Tarski Paradox
8:38
A playlist of the Probability Primer series is available here:
You can skip the measure theory (Section 1) if you're not interested in the rigorous underpinnings. If you choose to do this, you should start with (PP 1.S) Measure theory: Summary at:
(0:00) Intro to Probability Primer series.
(1:20) Why do we need measure theory? We illustrate the need using the remarkable Banach-Tarski Paradox.
0. Banach Tarski Banach Tarski
27:19
A teaser introduction to measure theory, motivated by the infamous Banach-Tarski paradox.
The Banach-Tarski Paradox
13
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows a constructive version of the Banach?Tarski paradox, discovered by Jan Mycielski and Stan Wagon. The three colors define congruent sets in the hyperbolic plane ?, and from the initial viewpoint the sets appear congruent to our E...
Contributed by: Stan Wagon
Audio created with WolframTones:
The Banach-Tarski Paradox
56
This video is an example based on the theory THE BANACH TARSKI PARADOX
Which says that a new substance can be formed by the rearrangement of substances in a object without losing anything.
A taste of abstract mathematics - Banach-Tarski Paradox
2:24
In this video, we explore a famous paradox in mathematics that sounds absolutely absurd - the Banach-Tarski Paradox. Simply put, the paradox stays that a sphere can be chopped up into finitely many pieces and reassembled into two copies of the original sphere!
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Real analysis, measure theory, Lebesgue measure, Banach-Tarski paradox, Banach, Tarski, set theory, abstract mathematics
A Friendly Introduction to Transfinite Arithmetic and the Banach-Tarski Paradox | Part 1
13:31
Link to my paper on it if you want to read it instead of hearing an awkward physics/math kid talk about it
What is The Banach Tarski Paradox
2:37
Hey guys! Today we’re talking about the Banach Tarski Paradox. It’s a paradox of uncountable infinity. Watch more to learn more!
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Banach-Tarski Paradox
1:00
I reconstructed a model of the Banach-Tarski's Chocolate Bar paradox and I show how it is also not what it seems.
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The Banach-Tarski Paradox
3:39
Today we take a look at the fascinating Banach-Tarski Paradox, and the infinite chocolate paradox.
Making Infinite Copies – The Banach-Tarski paradox – A Spiritual Implication
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Mathematical Marvels: the Banach-Tarski Theorem
2:28
In this video I look at some of the weird and wonderful things that happen because of the Axiom of Choice, including the famous Banach-Tarski Theorem. Once again, many thanks to Theo T-Rex Reynolds for doing the filming.
Banach Tarski Video
3:29
This is just a rough draft, pls not hate...
mod01lec02 - Infinite Sets and the Banach-Tarski Paradox - Part 1
15:48
Infinite Sets, Equinumerosity, Cantor's theorem, Cantor-Schroeder-Bernstein theorem
The Banach-Tarski Paradox
13
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows a constructive version of the Banach-Tarski paradox, discovered by Jan Mycielski and Stan Wagon. The three colors define congruent sets in the hyperbolic plane ?, and from the initial viewpoint the sets appear congruent to...
Contributed by: Stan Wagon
Audio created with WolframTones:
A Friendly Introduction to Transfinite Arithmetic and the Banach-Tarski Paradox | Part 4
4:59
Link to my paper on it if you want to read it instead of hearing an awkward physics/math kid talk about it
A Friendly Introduction to Transfinite Arithmetic and the Banach-Tarski Paradox | Part 3
15:02
Link to my paper on it if you want to read it instead of hearing an awkward physics/math kid talk about it
The Banach–Tarski Paradox, but backwards
24:14
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The Banach Tarski paradox
15:07
The Banach-Tarski Theorem
12:20
We describe the Banach-Tarski Theorem as a way of providing our first hint of non-measurable sets; and a further reminder of the distinction between real numbers and physical reality.
A Friendly Introduction to Transfinite Arithmetic and the Banach-Tarski Paradox | Part 2
14:35
Link to my paper on it if you want to read it instead of hearing an awkward physics/math kid talk about it
The Banach-Tarski Paradox
09
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This animation shows a constructive version of the Banach-Tarski paradox, discovered by Jan Mycielski and Stan Wagon. The three colors define congruent sets in the hyperbolic plane H, and from the initial viewpoint the sets appear ...
Contributed by: Stan Wagon (Macalester College)
Tackling the Banach-Tarski Paradox
3:01
This video, created for the Breakthrough Junior challenge, explains the Banach-Tarski Paradox.
#breakthroughjuniorchallenge
The breakthrough junior challenge THE BANACH TARSKI PARADOX
3:01
hello people, i present to you the explanation of the banakh tarski paradox hope you like it .
The Banach-Tarski Paradox
12:09
The Banach-Tarski paradox | Andrzej Zuk | Лекториум
33:31
The Banach-Tarski paradox | Лектор: Andrzej Zuk | Организатор: Математическая лаборатория имени П.Л. Чебышева СПбГУ
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mod01lec03 - Infinite Sets and the Banach-Tarski Paradox - Part 2
20:51
Problem of measuring subsets of R^n, Axiom of Choice and the Banach-Tarski Paradox, Violation of Finite-additivity
Banach- Tarski Paradox
11:14
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BANACH-TARSKI PARADOX
12:18
it's the spheres Bois
Matematikrevyen 2011: Banach-Tarski
3:43
The famous Banach-Tarski paradox, now in real life. Watch out as oranges multiply to powers of two. And don't forget to look it up on wikipedia:
Banach-Tarski Paradox
35
In this video I will be showing you how the Banach-Tarski Paradox can actually work in real life!!!
Banach-Tarski
1:18
Algorithm for doing N jobs:
def perform(tasks):
if len(tasks) == 0:
return True
if len(tasks) == 1:
do_work(tasks[0])
return True
end = len(tasks)
mid = end / 2
perform(tasks[0:mid])
perform(tasks[mid:end])
return True
The banach-tarski paradox #Race2space2021 #Race2space
3:43
Banach-Tarski Paradox
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Btw, other YouTubers also made videos on this topic, so you don't have to comment about it.