In electronic circuits require constant voltage. Would not be necessary to make the voltage at output of LM317T down to 0 volt. However, in the experiments will be necessary to adjust the the voltage. The IC LM317T, there is a weakness in this is the output the voltage minimum adj pin is connected to ground is equal to 1.25 volts.
But there are tricks to make LM317T adjustable voltage output is 0 volts. By creating a lower reference voltage to 0 volt to 1.25V (-1.25 volt). Then to the adj Will be able to adjust the output the voltage to 0 volt.
The negative voltage regulated IC number LM337T as same is if adj pin connect to ground will get lowest output voltage into -1.25 volt. Which if adjust as 0 volt reference voltage of +1.25 volts, it must be connected to the adj pin of the IC only.