I Question about transfinite numbers

Thread starter brianhurren
Start date Dec 17, 2022
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Numbers Transfinite

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The discussion centers on the existence of transfinite geometry, with participants expressing skepticism about its validity. While there is geometry in infinite-dimensional spaces, such as Hilbert spaces, some argue that this does not qualify as transfinite geometry. The consensus leans towards the idea that transfinite geometry, as a distinct concept, does not exist. The conversation highlights the complexities of geometry in infinite dimensions versus the notion of transfinite numbers. Ultimately, the participants conclude that transfinite geometry is not recognized in current mathematical frameworks.

Dec 17, 2022

brianhurren

just a simple question, is there such a thing as Transfinite geometry?

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Dec 18, 2022

Hornbein

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There is geometry in infinite dimensional spaces. I would opine that Hibert spaces don't count as transfinite geometry.

Dec 18, 2022

Mark44

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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.

Thread 'There are only finitely many primes'

I just saw this one. If there are finitely many primes, then ##0<\prod_{p}\sin(\frac\pi p)=\prod_p\sin\left(\frac{\pi(1+2\prod_q q)}p\right)=0## Of course it is in a way just a variation of Euclid's idea, but it is a one liner.

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