Solution to Rahul left his cycle in a parking lot that is filled with bikes and cycles, … - Sikademy
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Archangel Macsika

Rahul left his cycle in a parking lot that is filled with bikes and cycles, parked neatly in several rows. When he returns, he notices someone push all the vehicles on the left end of each row, causing them to fall. Rahul knows that if a bike falls, then the vehicle to its immediate right will also fall, but if a cycle falls, then the next vehicle will fall only if that is also a cycle. Rahul hasn’t spotted his cycle yet, but he deduces by mathematical induction that it will fall. “Let P(n) statement: ‘In every row, every cycle in nth position will fall.’ I know that P(1) is true - all cycles in the first position were pushed. For the inductive step, consider any row with a cycle in the nth position. By the inductive assumption, this cycle will fall. Now consider the next vehicle, which is in the (n + 1) th position. If it is a bike, I don’t have to prove anything; if it is a cycle, it will fall because it was pushed by the cycle on its left. ” What is the flaw in his argument?

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Mathematical induction is for every natural number, without breaks.

In the given proof Rahul does not consider bike in (n+1)th position.

But if cycles in (n)th position is falling and there is a bike in (n+1)th position, then this bike is not falling. So, cycles after this bike are not falling also.

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