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Temperature is the measure of the average kinetic energy of the particles of a substance. At absolute zero the kinetic energy of the particles is zero, ie they stop moving. Because you can't have negative kinetic energy, you can't go past zero.
0 kelvin is the lowest possible temperature. Absolute zero is defined as 0 kelvin, which is the lowest possible temperature. Also it may be easier to remember that kelvin is a absolute Temperature scale so absolute 0 logically would mean 0 K.
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