Is the Banach-Tarsky Paradox the End of Mathematics?

• eljose79
In summary, the conversation discusses the concept of complex numbers and their relevance in mathematics and physics, as well as the Banach-Tarsky paradox. It also questions the intentions and motivations behind the development of complex numbers in mathematics.

eljose79

i find it is imposible..in fact there is more matter in the end that in the principle...

o...k...

Do you mean that i is an impossible number

i2 = -1

It is physically impossible but mathematically it is a number, albeit a complex one.

Remember the study of complex numbers eventually lead to the development of the mathematics of flight for example. Just because it seems useless doesn't mean it is.

Originally posted by eljose79
i find it is imposible..in fact there is more matter in the end that in the principle...

Are you referring to the Banach-Tarsky paradox (one sphere becoming to spheres)?

Please try to post on the corresponding topic, so people know what you are talking about.

end of mathematics ever,
or,
end=aim (would mean physicists/mathematicians deliberately thinking out queer and funny numbers, operators, axioms, methods, just for fun or tinker arguments for their theories, ignoring the principles in nature)?
or,
do you just not like maths? :)

1. What is the Banach-Tarsky paradox?

The Banach-Tarsky paradox is a mathematical paradox that states that it is possible to take a solid sphere, divide it into a finite number of pieces, and then rearrange those pieces to form two identical copies of the original sphere. This means that, theoretically, it is possible to duplicate an object without adding or removing any material.

2. How is this paradox possible?

The Banach-Tarsky paradox is possible due to the fact that the pieces used to form the two identical spheres are non-measurable, meaning they do not have a defined volume. This allows for the pieces to be rearranged in such a way that they appear to have doubled in number, resulting in two identical spheres.

3. Who discovered the Banach-Tarsky paradox?

The paradox was first discovered in 1924 by two Polish mathematicians, Stefan Banach and Alfred Tarski. They published their findings in a paper titled "Sur la décomposition des ensembles de points en parties respectivement congruentes", which translates to "On the decomposition of sets of points into congruent parts".

4. What real-world applications does this paradox have?

The Banach-Tarsky paradox is purely a theoretical concept and does not have any practical applications. However, it has sparked important discussions and debates within the fields of mathematics and philosophy, particularly in relation to the concept of infinity and the nature of physical reality.