Dec 26, 2012 · The Archimedean property states that if $x$ and $y$ are positive numbers, there is some integer $n$ so that $y < nx$. This is a property of the real number field.

Nov 1, 2023 · When building the foundations of a subject you have to start somewhere. Quite often there are alternative places to start which turn out to be equivalent once they are understood. It is more …

The Archimedean property states that $\Bbb N$ isn't bounded above--some natural number can be found such that it is greater than some specified real number. The Archimedean property also states …

Proof of archimedean property Ask Question Asked 11 years, 8 months ago Modified 1 year, 1 month ago

I think I've understood that the Archimedean axiom is added in order to discard ordered complete fields containing infinitesimals like the hyperreal numbers. Additionally, this property clearly cannot be …

This is kind of a general question concerning the Archimedean property in the context of real analysis. I understand that for every real number, there exists a natural number that is greater than or

Jul 31, 2022 · I was wondering, if you have a simple Archimedean spiral, defined as : $ r=b\times \theta $ , with the angle $ \theta $ going from $ 0 $ to $ \Theta$ If you consider the spiral as a succession …

Apr 1, 2023 · This has nothing to do with prime ideals. Think of it as reasoning by analogy if you want. Or think of prime ideals in terms of extending non-archimedean absolute values if you want finite …

Oct 16, 2023 · Curvature of the archimedean spiral Ask Question Asked 2 years, 3 months ago Modified 2 years, 3 months ago

Apr 9, 2018 · @Lubin I deleted my comment after checking out Milne's notes. By discrete, Milne literally means that the image of the absolute value is discrete. By non-archimedean, he means that the …