Confusion with regards to units in Sinc pulse I am currently reading a section in the Handbook for MRI Pulse Sequence book where it says that the time-bandwidth product for a SINC pulse is given by:

$$
T \Delta f = Z 
$$

where $T$ is the length of the pulse, $\Delta f$ is the bandwidth and $Z$ is the number of zero crossings of the SINC pulse. Now, my question might be very naive but it says that this is a dimensionless quantity but I do not understand why that will be:

For example, if the bandwidth is described in radians/sec, does it not have units of radians? In that case, how does it relate to the number of zero crossings, which is indeed a discrete number.
The length of the pulse, $T$, would be in units of time (for example, in seconds). The bandwidth would be in units of frequency (for example, in Hz). So

$$[T][\Delta f]=sec\frac{1}{sec}=1$$

That means that $Z$ is a dimensionless quantity. That makes sense, as $Z$ is just a natural number that describes the number of times that something happens (in this case, the number of zero crossings), and should not have units at all.