## The Banach–Tarski Paradox

The mathematical study of infinity includes many surprising results and paradoxical conclusions. VSauce explains the Banach-Tarski Paradox.

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# Video Genre: Philosophy

## The Banach–Tarski Paradox

## How An Infinite Hotel Ran Out Of Room?

## Roger Penrose – Is Mathematics Invented or Discovered?

## What Is Luck?

## David Gross – Is Mathematics Invented or Discovered?

## Paul Davies – Is Mathematics Invented or Discovered? – First Part

## Paul Davies – Is Mathematics Invented or Discovered? – Second Part

## Is Time Travel Possible?

## How Big is Infinity?

## Max Tegmark – Is Mathematics Invented or Discovered?

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The mathematical study of infinity includes many surprising results and paradoxical conclusions. VSauce explains the Banach-Tarski Paradox.

If there's a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The answer is yes.

- Big Questions ,
- Mathematics ,
- Paradox ,

Sir Roger Penrose is an English mathematical physicist, mathematician, philosopher of science and Nobel Laureate in Physics.

Is luck real? It might feel like a mystical force tugging us toward good or bad fortune, but it turns out luck is really where probability runs into the human…

David Gross is a theoretical physicist and string theorist. He was awarded the 2004 Nobel Prize in Physics for their discovery of asymptotic freedom.

Paul is a physicist, writer and broadcaster, a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science.

Paul is a physicist, writer and broadcaster, a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science.

Time travel is a staple of science fiction stories, but is it actually possible?

- Big Questions ,
- Philosophy ,
- Science ,

Using the fundamentals of set theory, explore the mind-bending concept of the “infinity of infinities” — and how it led mathematicians to conclude that math itself contains unanswerable questions.

Max Tegmark is a physicist, cosmologist and machine learning researcher. He is a professor at the MIT and the scientific director of the Foundational Questions Institute.

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