Why voltage across capacitor cant change instantaneously?

Capacitors resist change in voltage. By definition, the equation is dv/dt = i/c, or rate of change of voltage in volts per second is current in amps divided by capacitance in farads. In order for the voltage to change instantaneously, then dv/dt must be infinity, which means i/c is also infinity. If capacitance is non-zero, then current must be infinity. Since there is no perfect voltage source, or no resistor or wire with perfect zero ohms, then it is impossible to have an infinite current, so it is impossible for the voltage across a capacitor to change instantaneously.