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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
- Proof of infinite monkey theorem. - Mathematics Stack Exchange
The infinite monkey theorem states that if you have an infinite number of monkeys each hitting keys at random on typewriter keyboards then, with probability 1, one of them will type the complete works of William Shakespeare
- 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
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 1 month 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"
- intuition - One divided by Infinity? - Mathematics Stack Exchange
$\begingroup$ Arithmetic with $\infty$ is usually a convention rather than a piece of mathematics (For example, some mathematicians (in measure theory) take $\infty\cdot 0 = 0$ and reason that this should be the case since $\infty\cdot 0$ represents the "area" of an infinite line in the plane with $0$ width and hence should be $0$ since area = height$\times$ width)
- How can I define $e^x$ as the value of infinite series?
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- 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 :-
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