S12
Infinity & Limits
Approach → Limit
"If you can get arbitrarily close, you can define the limit."
Philosophical Origin：Weierstrass epsilon-delta
Minimal Example
1/2 + 1/4 + 1/8 + ... approaches 1, never exceeds it.
One-Line Rule
"Infinity is a process, not a number."
Common Misconception vs Correct Understanding
Infinity is the biggest number.
Infinity is unbounded growth.
🌱 Growth Steps (Natural Evolution)
1 / 5 步
1
Sequence: Ordered list
✨ Starting Point: Growth begins here
如果你能 ↑ 那么你就能 ↓
2
Convergence: Approaches a value
如果你能 ↑ 那么你就能 ↓
3
Limit: The value approached
如果你能 ↑ 那么你就能 ↓
4
Infinite series: Sum of infinite terms
如果你能 ↑ 那么你就能 ↓
5
Continuity: Limit equals value
SAT Example Question
Question:
What does 0.999... equal?
Answer:
1
Explanation:
Limit of the sequence is exactly 1
Practice Questions
5 questions with multiple solution methods
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