(ELI5) How did the Mathematical Limit solved Zeno’s paradox?
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Zeno’s paradox was based on a fundamentally flawed assumption…that an infinite sum (a summation with an infinite number of terms) couldn’t add up to a finite number.
Figuring out mathematical limits gives a way to actually solve infinite sums. Specific to Zeno’s Paradox, it proved that 1/2 + 1/4 + 1/8 + … = 1. Not “close to 1”, not “kinda sorta infinitely close to 1”, not “infinity”, exactly 1.
So there’s no paradox. The arrow crosses an infinite number of steps in a finite time.
The mathematical concept of the limit helped solve Zeno’s paradox by showing that even though an infinite number of smaller steps can be divided, they can still sum up to a finite distance or time. By using the concept of limits, we can understand that the sum of an infinite series can converge to a definite value, allowing us to overcome the paradox of motion proposed by Zeno.
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