So I'm trying to understand this simple math formula, but I can't wrap my ahead about what it means to be an "inverse".
So for example, a CPU execution time for a program is given by the formula:
$$\text{CPU execution time} = \text{CPU Clock Cycles for a Program} \times \text{Clock cycle times}$$
But then they said clock rate and clock cycle times are inverses, and this is where I start to get confused. The clock rate is the frequency, and the clock cycle time is the time period for one clock cycle, which runs in a constant time. So how are they inverses? Because the above equation can be written as:
$$\text{CPU Execution Time} = \frac{\text{CPU Clock Cycles for a Program}}{\text{Clock Rate}}$$
$$f=\frac{1}{T}$$ $$T=\frac{1}{f}$$ Where $f$ is the frequency and $T$ is the time period of a cycle. This means that the reciprocal of the time period is the frequency and vice versa.