I need to know if the following has been deducted correctly. I am renown for making mathematical mistakes

but here it goes:

Prove that inertia can be given as the producct of inertial mass plus its relativistic mass. The case proven:

the small signature for the momentum is used as a trace of information, thus:

by rearranging:

So if you added the inertial mass in question (given any constant value) with the addition of some relativistic mass, then we have:

So naturally, we have used the upper case for momentum a relativistic gamma relation. If we remove the zero value of the gamma relations on both sides, we are left with this simple formula:

so we have an inertial mass from inviting a relativistic velocity minus its equivalent inertia. From here, the equation can be interpreted as how something has an inertial mass, and that is when you take the same quantity

and take it from the relativistic velocity, which zero, so all of this simplifies to a proof of Einsteins Weak Equivalence, so that:

Inertial mass is the same as the quantity of mass as well. Now since we are talking about mass and relativistic mass relationships, i now want to derive for density relationships. So following these derivatives, we use

wavelength of a thing as important as upon the sqaure of any wave, a density indeed can be given, but for the sake of simplicity, let us not get too entwined into that. Let's assume though the following, albeit as simple as it is:

solving yet again for the left hand side (warning, do not get mixed up where v is a volume.

which solves to

This should be seen as simple equating and rearranging, knowing that

. Does this all seem reasonable,

Thank in advance,

Manynames