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- calculus - What is infinity divided by infinity? - Mathematics Stack . . .
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 denominator: infinitesimal, infinite, or appreciable finite, before discussing the technical notion of limit which tends to be confusing to beginners
- limits - Can I subtract infinity from infinity? - Mathematics Stack . . .
$\begingroup$ Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like $\lim_{n\to\infty}(1+x n)^n,$ or is it just a parlor trick for a much easier kind of limit? $\endgroup$ –
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 2 months ago Modified 4 years
- elementary set theory - What do finite, infinite, countable, not . . .
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 sets are "at most countable"
- Uncountable vs Countable Infinity - Mathematics Stack Exchange
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 theoretically complete list of reals between 0 and 1 would not contain some numbers My friend understood the concept, but disagreed with the conclusion
- linear algebra - Definition of Infinite Dimensional Vector Space . . .
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 vector space or infinitely generated if there exists an infinite subset S of V such that L(S) = V I am having following questions which the definition fails to answer :-
- What exactly is infinity? - Mathematics Stack Exchange
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 cardinalities) For example, the set of integers is countably infinite, while the set of real numbers is uncountably infinite "-Wikipedia: Infinity
- Does infinite equal infinite? - Mathematics Stack Exchange
(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 $-\infty$ that have the largest magnitude of all infinite numbers, and do not obey the 'usual' laws of arithmetic)
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