lec-3.pdf

# lec-3.pdf - Today Principle of Induction(continued Today...

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Today. Principle of Induction.(continued.)

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Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 )
Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 )

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Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get...
Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) .

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Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) . ...Yes for 0,
Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) . ...Yes for 0, and we can conclude

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Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) . ...Yes for 0, and we can conclude Yes for 1...
Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) . ...Yes for 0, and we can conclude Yes for 1... and we can conclude

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Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) . ...Yes for 0, and we can conclude Yes for 1... and we can conclude Yes for 2...
Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) . ...Yes for 0, and we can conclude Yes for 1... and we can conclude Yes for 2 .......

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Today. Principle of Induction.(continued.) P ( 0 ) ( n N ) P ( n ) = P ( n + 1 ) And we get... ( n N ) P ( n ) . ...Yes for 0, and we can conclude Yes for 1... and we can conclude Yes for 2 .......
Last time.

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Last time. “But aren’t you starting with the statement to prove the statement?”
Last time. “But aren’t you starting with the statement to prove the statement?” In general, n N P ( n ) 6≡ P ( n + 1 ) .

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Last time. “But aren’t you starting with the statement to prove the statement?” In general, n N P ( n ) 6≡ P ( n + 1 ) . P ( n ) ” is “different” statement than “ P ( n + 1 ) ” for any fixed n .
Last time. “But aren’t you starting with the statement to prove the statement?” In general, n N P ( n ) 6≡ P ( n + 1 ) . P ( n ) ” is “different” statement than “ P ( n + 1 ) ” for any fixed n .

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Last time. “But aren’t you starting with the statement to prove the statement?” In general, n N P ( n ) 6≡ P ( n + 1 ) . P ( n ) ” is “different” statement than “ P ( n + 1 ) ” for any fixed n . P ( n ) n 0 i = ( n )( n + 1 ) 2 .”
Last time. “But aren’t you starting with the statement to prove the statement?” In general, n N P ( n ) 6≡ P ( n + 1 ) . P ( n ) ” is “different” statement than “ P ( n + 1 ) ” for any fixed n . P ( n ) n 0 i = ( n )( n + 1 ) 2 .” P ( 2 ) 0 + 1 + 2 = ( 2 )( 3 ) 2 .”

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Last time. “But aren’t you starting with the statement to prove the statement?” In general, n N P ( n ) 6≡ P ( n + 1 ) . P ( n ) ” is “different” statement than “ P ( n + 1 ) ” for any fixed n .
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