Mathematical proof Definition and 61 Threads

For the twin paradox to be considered a true paradox the framing of the scenario must be stringent, that is to say we cannot permit assumptions to be ignored. Therefore I must start with a short description of the twin paradox followed by identification of the inherent assumptions. From...

Is there a mathematical proof that can prove that the integral is the antiderivative?

Hi, I have a pretty in depth understanding of special relativity. Recently I have been searching for mathematical proof of the Lorenz transformation. I found some information about it, but to tell the truth I didn't understand much of it. Maybe one of you guys can shed some light on the proof...

I've figured out a faster way of doing simple mixture problems; how do I mathematically prove it consistantly works? Edit: Is my question badly worded somehow? 30 people have looked at this; 0 have replied. Kind of awkward, but if you don't know what I'm trying to ask, or I need to give...

Current science describes a solid, liquid, and gas, as having different densities. Solids have the highest density, then comes liquids, and finally gases. They say in between the particles lies "empty space." Can someone please describe to me the properties of "empty space" because as fas as I...

Current science describes a solid, liquid, and gas, as having different densities. Solids have the highest density, then comes liquids, and finally gases. They say in between the particles lies "empty space." Can someone please describe to me the properties of "empty space" because as fas as I...

I'm given the statement: if m^2 is of the form 4k+3, then m is of the form 4k+3. I don't even know how to begin proving this. I'm guessing by contraposition.

I'm given the statement: if m^2 is of the form 4k+3, then m is of the form 4k+3. I don't even know how to begin proving this. I'm guessing by contraposition.

We are given the following statement: The universe is all integers. If a-3b is even, then a+b is even. I began off with saying that 3 cases exist: a is odd and b is even, a is even and b is odd, both a and b are odd, and both a and b are even. After this point I got really confused and lost...

I am trying to prove that \frac{d\langle p \rangle}{dt} = \langle -\frac{\partial V}{\partial x} \rangle I am done if I can just prove that \left[ \Psi^*\frac{\partial^2 \Psi}{\partial x^2} \right]_{-\infty}^{\infty} = 0 \left[ \frac{\partial \Psi}{\partial x} \frac{\partial...

Does anybody know how to mathematically prove that an object launched at a 45 degree angle will have the largest possible displacement?