Rigorous Definition and 160 Threads

First, please don't give me too much information or suggest other ways to do it if you think this is not rigorous. This is not supposed to be collaborative. I am asked to prove that n!^{n+1} divides (n^2)!. I thought of a few ways to try to do this, but the first thing I got is the...

The Background: I'm trying to construct a rigorous proof for the divergence theorem, but I'm far from my goal. So far, I have constructed a basic proof, but it is filled with errors, assumptions, non-rigorousness, etc. I want to make it rigorous; in so doing, I will learn how to construct...

Is there a "rigorous" proof.. -That a "Quantum" of space (a minimum lenght, area or volume for any 4-dimensional Manifold) exist applying Quantum mechanics and GR?..both together or in the "Semi-classical" limit?... - this "Planck lenght" should be obtained directly from math and never...

Well, I'm searching for a rigorous derivation of the famous "perihelium precession problem in General Relativity". Did anyone do it...? Daniel.

Hi: I would like to get a mathematically rigorous "introduction" to QM. Which books would you recommend?

What is the mathematicians modern rigorous definition of number ? thanks Roger

Hi I'm looking for the mathematically rigorous definition of time ? can anyone help me ? Thanks Roger

Hi I hope someone can help me with this : I need the rigorous proof for 1+1 = 2 and explained in a fairly simple way. Thanks Roger

The SimCity navy has a rigorous training program. In order to graduate from the naval academy, cadets must enter a pool and fight sharks. Today, a group of cadets was tested. Each cadet put on his mask, snorkel, and two flippers; and armed himself with a knife. Then the cadets jumped into the...

I think I understand the formal/rigorous definition of limit, but I find proving various limits (or following proofs of them) extremely difficult. I hope you all will help me. I think I won't advance my calculus study until I really get this limit proving thing btw... Here's one limit prove...