A.1 · 3 · Enrichment · mathematics and Theory of Knowledge
Zeno: is all motion an illusion?
An ancient paradox, settled by a series that adds to a finite number.
SL+HLMedium12 minFree
Hook
To walk from A to B you must cover half the distance, then half of what is left, then half again, forever. So how does anyone arrive?
Zeno of Elea
1 / 4
Check 1 of 3
A convergent series…
Check 2 of 3
After 3 terms of ½ + ¼ + ⅛ + …, the total is…
Check 3 of 3
What is wrong with "infinite steps need infinite time"?
Apply
In two sentences, explain how a convergent series settles Zeno’s paradox.
Your writing is saved on this device.
Remember earlier lessons
From lesson A.1 · 2
Frequency is…
From lesson A.1 · 1
Motion is relative because…
Summary card
Key points
- • Zeno claimed infinite steps mean infinite time.
- • ½ + ¼ + ⅛ + … converges to 1.
- • Convergent: finite. Divergent: infinite.
Formulas
- Sₙ = 1 − (½)ⁿ
Key terms
- Convergent :
- the sum is finite
- Divergent :
- the sum grows without limit
Common errors
- • Thinking infinitely many terms must sum to infinity.
Checks solved: 0 of 3