Look at the atached data sheet for your LM339 and find the schematic diagram for it. Now look at the output, pin 3. Follow it back to the collector of Q8, the output transistor. Note that there is no connection between Q8's collector and anything. Not being connected to anything, the LM339 can not have an output voltage by itself.
The pullup resistor completes the circuit between the output transistor and the 5 volt power source allowing the LM339's output to toggle between 0 and 5 volts.
http://www.fairchildsemi.com/ds/LM/LM339.pdf
The pullup resistor completes the circuit between the output transistor and the 5 volt power source allowing the LM339's output to toggle between 0 and 5 volts.
http://www.fairchildsemi.com/ds/LM/LM339.pdf