0
votes
2answers
33 views

Countably or Uncountably Many Discontinuities

I want to know why the following function has uncountably many discontinuities: $$f(x)=\left\{\begin{array} & x^2 & x \not \in \mathbb{Q} \\ 0 & \text{otherwise} \end{array}\right .$$ ...
2
votes
2answers
102 views

Is an infinitely small percentage of infinity infinite?

I'm not a mathematician, but this question intrigues me: Is an infinitely small percentage or part of infinity infinite? Do the two infinities "cancel out", leaving you with a real number? It seems ...
12
votes
5answers
2k views

One divided by Infinity?

Okay, I'm not much of a mathematician (I'm an 8th grader in Algebra I), but I have a question about something that's been bugging me. I know that $0.999 \cdots$ (repeating) = $1$. So wouldn't $1 - ...
21
votes
4answers
952 views

You are standing at the origin of an “infinite forest” holding an “infinite bb-gun”

I use stories like these to develop intuition... or perhaps to destroy it. I have my own answers in mind, but I want to see if I have made any mistakes... You are standing at the origin of an ...
2
votes
2answers
471 views

Understanding of convergence of intersections of sets

If you start with an infinite set, you can have a sequence of nested sets which converge to a single point. (ie Intersection of (-1/n, 1/n) as n->infinity)) However, at no time during the sequence is ...