According to the theory of relativity, as an object with mass approaches the speed of light, its energy and momentum increase without bound. However, the mass of the object also increases, which requires more and more energy to accelerate it further. As the object gets closer and closer to the speed of light, the energy required to accelerate it becomes infinitely large, making it impossible to reach or exceed the speed of light.
Electrons are particles with mass, and they follow the same principles described by the theory of relativity. No matter how much energy is imparted to an electron, it would require an infinite amount of energy to accelerate it to the speed of light. As a result, electrons, like any other object with mass, cannot attain infinite speed.
Additionally, at speeds close to the speed of light, time dilation and length contraction effects become significant. These effects cause time to appear to slow down for the moving object and lengths to appear shorter in its direction of motion, as observed from a stationary reference frame. These relativistic effects further prevent an object from reaching or exceeding the speed of light.
Therefore, based on our current understanding of physics and the theory of relativity, electrons (and any other objects with mass) cannot achieve infinite speed.