Is frequency for dc zero Hz?
Very clever, but that's not how it works.  

By your reasoning you should not only be able to make the frequency infinite, but also 4 Hz, or 100 Hz, or \$\sqrt{2}\$ Hz, all at the same time, with the same signal. And that's why you can't do that: a repeating signal can have only 1 fundamental frequency, which is 1/period.

It would be the same as taking 2 periods of the 4 Hz sine and saying that that's the period, because it also repeats, and then the signal would be 2 Hz. It can't be 2 Hz and 4 Hz at the same time.