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- set theory - Hilberts Grand Hotel is always hosting the same infinite . . .
From an excellent answer here, I gather that 1 is taken to mean that the hotel is hosting an infinite set of guests and that 2 means things have changed, we now have to reassign every room again to accommodate a new infinite set of guests (eg: the ones before + 1) I saw other threads and answers But the "new" set is just the same old set
- general topology - Why is the infinite sphere contractible . . .
Why is the infinite sphere contractible? I know a proof from Hatcher p 88, but I don't understand how this is possible I really understand the statement and the proof, but in my imagination this
- One divided by Infinity? - Mathematics Stack Exchange
Infinite decimals are introduced very loosely in secondary education and the subtleties are not always fully grasped until arriving at university By the way, there is a group of very strict Mathematicians who find it very difficult to accept the manipulation of infinite quantities in any way
- 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 infin
- elementary set theory - What do finite, infinite, countable, not . . .
What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago
- elementary set theory - What is the definition for an infinite set . . .
However, while Dedekind-infinite implies your notion even without the Axiom of Choice, your definition does not imply Dedekind-infinite if we do not have the Axiom of Choice at hand: your definition is what is called a "weakly Dedekind-infinite set", and it sits somewhere between Dedekind-infinite and finite; that is, if a set is Dedekind
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 6 months ago Modified 4 years, 9 months ago
- What is the difference between infinite and transfinite?
The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about $\infty$ or infinite cardinals somehow, which may be giving the wrong impression But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes
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