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Lab · c03.s03.L1

Induction dominoes

Induction reaches every case only when a base case starts the chain and each step carries from one case to the next.

Question: When does assuming the previous case help?

Induction dominoesTwelve upright dominoes labelled S_0 through S_11 stand in a row on cream paper. With the base case proved, the first is pushed and each falling domino knocks the next, until all twelve lie flat and the panel reports every case established. With the base case not proved, none fall. With the step after S_5 broken, the first six fall and the last six stay upright. Induction needs both a base case and every step.Induction dominoesWhen does assuming the previous case help?Base case provedStep: no breakS_0S_1S_2S_3S_4S_5S_6S_7S_8S_9S_10S_11Prove the base case, and prove that each case carries to the next.Established 0 of 12 · Standing 12
Schematic Schematic: twelve dominoes stand for the statements S_0 to S_11. The frames show the base case starting the chain, one step failing, and every later case staying unproved. The counts are exact consequences of the stated chain rule, computed by data/scripts/c03.s03.L1.py, not measured data.
Lab controls
base case proved

Left and Right toggle; Space or Enter toggles when the control has focus; B toggles from anywhere in the lab

no break

Left and Right move one option; Page Up and Page Down move five; Home selects no break; End selects break after S_10

Frame 1 of 9: Two obligationsAll twelve dominoes stand upright, the base case is proved and no step is broken. Induction asks for two things: prove the base case, and prove that each case forces the next. Nothing has fallen yet.

Keyboard: Space plays or pauses, Left and Right step, Home goes to the first frame, End goes to the last frame.

Text description of this lab

Twelve upright dominoes labelled S_0 through S_11 stand in a row on cream paper. With the base case proved, the first is pushed and each falling domino knocks the next, until all twelve lie flat and the panel reports every case established. With the base case not proved, none fall. With the step after S_5 broken, the first six fall and the last six stay upright. Induction needs both a base case and every step.

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Caption status: schematic. Every lab declares one of published, re-simulated, schematic, synthetic or interpolated.