Question about transfinite numbers

In summary, transfinite numbers are numbers that represent quantities greater than any natural or finite number, including infinity. They are different from other numbers because they can represent infinite quantities. In mathematics, they are significant for the study of infinite and uncountable sets, and they have practical applications in fields such as computer science, physics, and economics. While they were initially a theoretical concept, they have proven to be useful in various practical applications as well.
  • #1
brianhurren
71
2
just a simple question, is there such a thing as Transfinite geometry?
 
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  • #2
There is geometry in infinite dimensional spaces. I would opine that Hibert spaces don't count as transfinite geometry.
 
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  • #3
Hornbein said:
There is geometry in infinite dimensional spaces.
I agree, but I don't think that there is such a thing as transfinite geometry.
 

FAQ: Question about transfinite numbers

What are transfinite numbers?

Transfinite numbers are numbers that are larger than any finite number but smaller than infinity. They were first introduced by mathematician Georg Cantor in the late 19th century.

How are transfinite numbers different from regular numbers?

Transfinite numbers are different from regular numbers because they can be used to represent infinite quantities, while regular numbers can only represent finite quantities. They also follow different rules and properties than regular numbers.

What is the significance of transfinite numbers?

The significance of transfinite numbers lies in their ability to represent and understand the concept of infinity in mathematics. They have also been used in various fields such as set theory, topology, and analysis to solve complex problems and paradoxes.

Can transfinite numbers be used in real-world applications?

Yes, transfinite numbers have been used in real-world applications such as computer science, economics, and physics. They have been used to model infinite processes and to solve problems involving infinite quantities.

Are there different types of transfinite numbers?

Yes, there are different types of transfinite numbers, including aleph numbers, beth numbers, and the surreal numbers. Each type has its own unique properties and uses in mathematics and other fields.

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