You are correct that the concept of infinity, as used in mathematical reasoning, is not directly defined in physics. When discussing the impossibility of traveling faster than the speed of light, it is more accurate to rely on the principles and equations of physics, specifically the theory of relativity.
In the theory of relativity, the impossibility of exceeding the speed of light arises from the fundamental postulates and mathematical formulations of the theory. It is not solely based on invoking infinity as a mathematical concept. The theory of relativity provides a consistent framework for understanding the behavior of objects with mass and the propagation of light, and it has been extensively tested and confirmed by experimental observations.
According to the theory of relativity, as an object with mass approaches the speed of light, its relativistic mass increases, and the amount of energy required to accelerate it further also increases. As the object approaches the speed of light, its relativistic mass would tend towards infinity, and it would require an infinite amount of energy to accelerate it to or beyond that speed.
This conclusion is derived from the equations of special relativity, such as the Lorentz transformation and the relativistic momentum-energy relation, which do not explicitly involve the concept of infinity. These equations account for the effects of time dilation, length contraction, and the conservation of energy and momentum in relativistic scenarios.
Therefore, while the concept of infinity may be used in some mathematical explanations, the impossibility of surpassing the speed of light is firmly grounded in the principles and mathematical formulations of the theory of relativity itself, rather than relying solely on the notion of infinity.