I would be interested in some comments on this. Note that I am more or less thinking out loud here.
An ideal particle is moving through an ideal one dimensional Euclidean space bounded [0,1] and initially its location is 0.
The space is modelled by real numbers and in real numbers there is no next number.
I am assuming the passing of time and that the particle is located in the present with a location 0.
So if this particle is to make any progress at all towards the end of the path this will entail that its location must change and it can only be that it moves by a finite, infinitely divisible interval because the location (distance from 0) would change to another real number and any two real numbers differ from each other by a finite, infinitely divisible interval.
On the other hand, if we don't assume anything about time passing and this is just a line segment then it will cover every single value in the range [0,1].
An ideal particle is moving through an ideal one dimensional Euclidean space bounded [0,1] and initially its location is 0.
The space is modelled by real numbers and in real numbers there is no next number.
I am assuming the passing of time and that the particle is located in the present with a location 0.
So if this particle is to make any progress at all towards the end of the path this will entail that its location must change and it can only be that it moves by a finite, infinitely divisible interval because the location (distance from 0) would change to another real number and any two real numbers differ from each other by a finite, infinitely divisible interval.
On the other hand, if we don't assume anything about time passing and this is just a line segment then it will cover every single value in the range [0,1].
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