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You also appear unclear on the concept of the term "
infinite" as a measure of quantity independent of the variable "time". Such a
concept does exist.
For example,
- some mass with some distance from another mass is said to have a finite amount of potential energy related to the gravitation between them. The conversion of this potential energy into kinetic energy is limited over time by the maximum velocity of the masses (the speed of light)
- but it is also limited independant of time based on the two masses and the distance between them.
It is for the latter reason, and not the former, that such an energy source is considered "finite". Your energy source has not been declared to have any limit without considering the variable "time", and is therefore considered infinite. If one were able to successfully argue that time is finite, a different conclusion could be reached.