Do physicists talk about instants and infinitely small moments in time?
If so, how do they measure something like that? If they don't measure it, why do they think it exists?
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Time and space are modeled in most physics theories as continua because there is no evidence that they are discrete.
Models are just models. We may eventually discover, or become convinced theoretically, that time and space are discrete and not continuous.
An instant is not an infinitely-small time interval. It is a zero-size time interval, the analog of a point in space.