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The confusion here is that there are actually two commonly used definitions of mass in relativity.Relativistic mass follows E=mc2. This means as the energy of something goes up as it increases in speed, this mass goes up. This mass is basically a measurement of energy.Invariant mass follows E2-(pc)2=m2c4. This mass doesn't change a something speeds up, as it's equal to the mass you would measure if the object were at rest.It sounds like you're looking at equations of invariant mass, but thinking about relativistic mass.
i was always taught that the E in E=MC^2 was the energy in the object itself