Why does the infinite subdivision of Zeno's paradox result in a finite catch-up time?

Conditions

• Convergent geometric series
• $v_A = 2, v_T = 1$

Reasoning, step by step

1. Recognize that the time intervals form a geometric series with ratio $1/2$.
2. Sum the series $1 + 1/2 + 1/4 + \dots$ to get 2.
3. Verify using relative speed: Initial gap 2 divided by speed difference $(2-1)=1$ equals 2.
4. Conclude that the infinite sum converges to a finite value.

Example

The script states: 'These formulas illustrate that although there are infinitely many stages to the chase, both the aggregate space covered and the elapsed clock time remain bounded within finite limits... The series sums to a total time of 2... Infinitely many mathematical subdivisions have a finite endpoint; they are not infinitely many separate physical actions.'

Common misconceptions

• Believing that an infinite number of steps necessarily requires infinite time.
• Confusing mathematical subdivisions with separate physical actions that cannot be completed.

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