Before revision: Mathematically speaking, "time-invariance" of a system is the following property: Given a system with a time-dependent output function , and a time-dependent input function ; the system will be considered time-invariant if a time-delay on the input directly equates to a time-delay of the output function.
After revision: Mathematically speaking "time-invariance" of a system is the following property: Given a system with a time-dependent output function , and a time-dependent input function the system will be considered time-invariant if a time-delay on the input directly equates to a time-delay of the output function.