Recent content by kindlychung

If NxN has the same cardinality has N, then by definition there is a bijection between N and NxN.

How far and how wide? Is it possible to have multiple types of charge only two types of interaction between them?

Why are we so sure that there are only two types of electrical charge?

Homework Statement Is it possible to construct a sequence like this? If yes, please construct one, if not, give a proof. See the attached pic for requirements for the sequence to be constructed. Homework Equations NO The Attempt at a Solution I know how to construct a sequence that...

This is an analysis exercise, I don't get the definition of S. Could anyone explain, please? See the attached pic.

Okay, I think I got it. Let m, n be any positive integers, any positive element q of Q can be written as m/n, and any negative element q of Q can be written as -m/n. Let's define function f as follows: f(q) = \frac{q_{1}+q_{2}}{2} + \frac{q_{2}-q_{1}}{2}\cdot\frac{m}{m+n} (q>0) f(q) =...

I have edited the original post. Please see. ((q1, q2) cap Q) is the set of all non-integer rational numbers between q1 and q2. By intuition I know it has the same cardinality as Q, yet I don't know how to build a 1-1 correspondence between it and Q, please help.

For any two rational numbers q1<q2, card ((q1,q2) cap Q) = card Q, right? How to prove it, if it's true?

This works: Manipulate[Plot[E^(n*x), {x, -10, 10}], {n, 1, 10}] This doesn't: f[x_] := E^(n*x); Manipulate[Plot[f[x], {x, 1, 10}], {n, 1, 10}] Why? (I used Mathematica 7.0)