Section 03 — Infinity & Limits

Course: LBS 110 – Mathematics for Modern Thinkers

Learning Session

Explore These Materials: 1. Read (45 min) — Zeno’s Paradoxes (overview); An intuitive introduction to limits (short notes).
2. Watch (60 min) — Visualizing convergence (bisection, 1/2 + 1/4 + …); When series diverge (harmonic series story).
3. Listen (30 min) — Infinity in math and philosophy (radio/podcast segment).
4. Reflect While Engaging — Note where “infinite processes” show up in your work (recursion, iteration, compression, approximation).

Key Quote Box

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Practice

1. Zeno Track — Mark a 10 m stretch; walk halfway, then half of what’s left, etc., for 6 steps. Record distances and sketch the pattern.
2. Numerical Limits — Compute the first 10 values of (1 + 1/n)^n and of (n/(n+1)); describe what each seems to be approaching.
3. Series Intuition — Sum the geometric series 1/2 + 1/4 + … + 1/2^k for k = 1..8; compare partial sums to 1.
4. Reflection — Where does “infinite” model reality well, and where is it a useful fiction?

Hard Problem (Optional)

Show that 0.999… = 1 using two different arguments (algebraic and limits/series). Explain what each argument is really saying.