Can something really be divided into an infinite number of parts? It seems like it's theoretically possible to infinitely continue dividing something, but that is in no way the same thing as saying that something can be infinitely divided at any point in temporality, since an infinite period of time must be reached before something has been infinitely divided (which is not even a theoretical possibility). It seems like vast claims and supposed paradoxes in physics and mathematics are founded on this dubious assumption that an object or shape can be theoretically divided into an infinite number of parts.

It may help to say that we only need "infinite divisibility"--we don't need the division to have actually taken place, only to be possible in principle.

Also, what is your model of "dividing" here? Do you imagine scissors and paper and a lot of cutting? Perhaps there are other ways of conceptualizing infinite division that don't require time.

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