Principle of Mathematical Induction/Informal Analogy
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When the first domino is knocked over, the entire line topples, one after the other.
It follows that if either:
- $(1) \quad$ no domino is knocked over to start with (that is, the basis for the induction does not hold)
- $(2) \quad$ the gap between two dominoes is too large for one domino to knocked over the next one (that is, the induction step does not hold)
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 3$: Natural Numbers: $\S 3.7$: Principle of induction
- 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.1$ Mathematical Induction