At standard pressure, the 0 degree celsius is like the equilibrium temperature. In other words, at exactly 0 degrees C, the solid and liquid phases coexist at an equilibrium. If you increase it you'd have a solid (freezing). If you decrease you'd have a liquid phase. You can toggle between the two by either increasing or decreasing. So ice and a cup of water can exist in the room indefinitely at thermal equilibrium.
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