Aug 11, 2012 · One advantage of approach (2) is that it allows one to discuss indeterminate forms in concrete fashion and distinguish several cases depending on the nature of numerator and …

Apr 28, 2016 · $\begingroup$ Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like …

Infinite Geometric Series Formula Derivation. Ask Question Asked 12 years, 2 months ago. Modified 4 years ...

Clearly every finite set is countable, but also some infinite sets are countable. Note that some places define countable as infinite and the above definition. In such cases we say that finite …

As far as I understand, the list of all natural numbers is countably infinite and the list of reals between 0 and 1 is uncountably infinite. Cantor's diagonal proof shows how even a …

Sep 24, 2020 · In the text i am referring for Linear Algebra , following definition for Infinite dimensional vector space is given . The Vector Space V(F) is said to be infinite dimensional …

Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called …

Jan 1, 2021 · Let us follow the convention that an expression with $\infty$ is "defined" (in the extended reals) if: when you replace each $\infty$ with any function/sequence whose limit is …

(the principal exception I know of is the extended hyperreal line, which has many infinite numbers obeying the 'usual' laws of arithmetic, and a pair of additional numbers we call $+\infty$ and $ …

Infinite numbers do exist in the hyperreal number system which properly extends the real number system, but then their reciprocals are infinitesimals rather than zero. Thus the idea of …