A 1V voltage source with a series resistance of 1 ohm can produce 1 amp into a short circuit. The terminal impedance looking into the voltage source and resistor is 1 ohm.
If you converted this circuit to a current source, your source would be 1A with a parallel resistance of 1 ohm. If you were to calculate the terminal impedance of that set-up it would be 1 ohm.
Both these circuits provide identical performance and functionality - if both were placed inside a box with their terminals coming out and you were asked to probe the terminals and measure this (and that) you would find zero electrical difference.
This means that the current source without the parallel resistor MUST have infinite impedance and, as is more commonly known, the voltage source (without the series resistor) has zero impedance.
Another way to look at a current source is as an infinite voltage source in series with an infinite resistance. Despite both voltage and resistor being infinite they can still have a ratio and if this ratio is 1 then the current source is 1 amp and no matter how little or much resistance you connected to the output terminals, 1 amp would always flow.