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 …

Proof of archimedean property Ask Question Asked 11 years, 7 months ago Modified 1 year ago

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 …

Jan 31, 2018 · Here is a solution for a double Archimedean spiral (see figure below). Let us consider the simplest Archimedean spiral with polar equation:

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 …

Proving the Archimedean principle first for R R, using the sup sup, is in a way cheating. This principle is already present in N N and should be proven from the Peano axioms.

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 …

Jan 20, 2022 · Different definitions of the archimedean property Ask Question Asked 3 years, 11 months ago Modified 3 years, 11 months ago

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 …