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.
I had a discussion with a friend about the monkey infinite theorem, the theorem says that a monkey typing randomly on a keyboard will almost surely produce any given books (here let's say the bible...
Except for $0$ every element in this sequence has both a next and previous element. However, we have an infinite amount of elements between $0$ and $\omega$, which makes it different from a classical infinite sequence. So what exactly makes an infinite sequence an infinite sequence? Are the examples I gave even infinite sequences?
What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 3 months ago Modified 13 years, 3 months ago
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 ...
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.
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...
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...
Infinite simply means "not finite", both in the colloquial sense and in the technical sense (where we first define the term "finite"). There is no technical definition that I am aware of for "transfinite". Nevertheless, I can attest to my personal use. Transfinite is good when there is a notion of order, so "transfinite ordinal", or when you want to talk about non-standard real numbers which ...
