There are no intinifesimals in Zeno’s paradox. Each step has a strictly finite length.
There are also no infinitesimals on the line segment. Each point has a size of exactly 0.
Of course, you cannot calculate the length of the segment based on this as L = point size number of points = 0 infinity, because infinity is not a number. You can’t pass to the limit of infinity before doing the multiplication unless you know that all multipliers are finite, which is not the case here. What you can do here is calculate N * (L/N) and pass to the limit N → infinity, in which case both your multipliers are always finite.
Always do the calculation first and then pass to the limit (unless you know that in your specific case it doesn’t matter—there are theorems for that, of course).
There are no intinifesimals in Zeno’s paradox. Each step has a strictly finite length.
There are also no infinitesimals on the line segment. Each point has a size of exactly 0.
Of course, you cannot calculate the length of the segment based on this as L = point size number of points = 0 infinity, because infinity is not a number. You can’t pass to the limit of infinity before doing the multiplication unless you know that all multipliers are finite, which is not the case here. What you can do here is calculate N * (L/N) and pass to the limit N → infinity, in which case both your multipliers are always finite.
Always do the calculation first and then pass to the limit (unless you know that in your specific case it doesn’t matter—there are theorems for that, of course).