# How does the temperature ever change? If we assume that temperature is a continuous measurement, then we know that it has an infinite number of potential values. In order for temperature to transition between two values, it must then pass over the infinite set of values that lies between whichever two values the temperature is transitioning between. It now seems that temperature should not be able to change at all because before it may change to a given value, it must first reach a value between the desired and the current. Since we can make this claim infinitely, it would seem that temperature becomes "trapped", in a sense, at its current value, unable to change at all. Of course this problem can be applied to other concepts as well, and we might easily draw comparisons to Zeno's ancient thought experiment of Achilles and the tortoise. But the logic here is slightly different; the desired temperature is not continuously fleeing from the present as the tortoise is from Achilles. I simply raise the question as to how Achilles would be able to change his position at all as long as we observe the concept of infinity.

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