I don't understand why this project has given rise to so much discussion. Wouldn't using a 9V battery:By applying a voltage without a current limiting resistor you are allowing high currents to flow through the LED -- provided the voltage source's internal resistance doesn't prevent it -- and it is the high current that does the damage. The resistor is there not to limit the voltage, but to limit the current. Of course, like in a resistor, the voltage and current in an LED is an invertible function (at a given temperature). If you tell me the voltage across it I can tell you the current through it and vice-versa (assuming I have the voltage-current characteristic for that LED).
- with an ~10kΩ resistor
- with 330/470Ω
- with no resistor