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question about batteries "current draw"

hi,

sorry if this is a noob question :D

suppose that i have 2x AA batteries "1000 mAh each one", can i attach to them a component that draws 1500 mA, or i am limited to 1000 mA, i mean am i limited to the current that one battery can provide "1000 mAh" or to the sum of the current of all batteries "2000 mAh"?