Considering a supposed infinite number of divisions of 1mm (or any other finite distance):
If each division has a width of 0 (hypothetically) – then after multiplying by infinity the resulting value = 0.
Each division must have a width greater than 0 – therefore after multiplying by infinity the resulting value = infinity.
A counterargument such as “don't multiply by infinity” is self-defeating, because it would simply mean the number of divisions being considered is not infinite.
This simple logic proves physical reality cannot exist as infinitely divisible.
“Infinity in an Inch” – Presented by: Chico the Philosurfer.
Considering time to be infinitely divisible during travelling any finite journey:
If each time period that exists between positional changes is 0, then anything that moves will be travelling at an infinite speed and would therefore travel an infinite distance in an instant.
Each time period that exists must actually be greater than 0... after multiplying by infinity, the time period will be infinite, and therefore no movement will occur.
Like for distance, a counterargument such as “don't multiply by infinity” is also self-defeating, because once again it would mean the number of divisions being considered is simply not infinite.
This simple logic proves that time cannot exist as infinitely divisible.
A more detailed look at time and distance – time actually equals distance (positional change): “Zeno's Paradoxes of Motion – Logical Analysis” – in particular refer to: “The Arrow – A Clock for Zeno”
A velocity of 1mm per second will take a 5mm journey 5 seconds to complete, of course.
But this is to simply consider divisions of time to be 1 second steps and divisions of distance to be 1mm steps. Such finite sizes are obviously not infinitely small and therefore no infinity analysis has occurred.
Regardless of whether all divisions of a finite value are equal in size, or if each division has a different size, the average division size equals: Finite size / Number of divisions – any finite value / infinity = 0... therefore to suggest that any finite value is infinitely divisible, is to suggest an average division size of 0, which is paradoxical in that it eliminates existence.
Photons travel at the speed of light (causality), which can be represented as travelling: 1 Planck length in 1 unit of Planck time.
Another example of movement is in computer graphics, whereby there are two basic options for varying the speed of objects, e.g., characters in a game:
Move a different number of pixels per frame.
Wait a different amount of time between frames.