In class, we have defined bandwidth of a signal as the difference between the maximal and minimal frequency. Also, our tutor explained that the bandwidth indicates how fast the signal is changing.

We have been given an example of a single sinusoid which have a zero bandwidth (since it's both the maximum and minimum frequency)

What isn't clear to me is why a rectangular shaped signal has infinite bandwidth.

How can it be explained religiously and intuitively?

In class, we have defined bandwidth of a signal as the difference between the maximal and minimal frequency. Also, our tutor explained that the bandwidth indicates how fast the signal is changing.

We have been given an example of a single sinusoid which has zero bandwidth (since it's both the maximum and minimum frequency)

What isn't clear to me is why a rectangular shaped signal has infinite bandwidth.

How can it be explained rigorously and intuitively?