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Your notes (did you take them?) aren't very helpful, as there is a relatively minor error in them -- a misplaced parenthesis.Robb said:Homework Statement
Attached are notes from class. Can someone please explain what happens to (-x(n+1)) in step 3 to step 4. Not sure why it goes away. Thanks!
Homework Equations
The Attempt at a Solution
Step 3 in proof by induction is used to show that the statement being proved holds for the next integer after the base case. This step is crucial in establishing the validity of the proof for all integers.
Step 3 is used to show that the statement holds for the next integer, while step 4 is used to show that the statement holds for all integers. Step 3 is a specific case of step 4, as it only applies to the next integer after the base case.
Step 3 is necessary in proof by induction because it bridges the gap between the base case and the general case. It shows that if the statement holds for one integer, it will also hold for the next integer, thus proving the statement for all integers.
The value for the next integer in step 3 is chosen based on the statement being proved. It should be the next integer after the base case that will help in proving the statement for all integers. This value is typically chosen by observation and understanding of the problem at hand.
No, step 3 cannot be skipped in proof by induction as it is a crucial step in establishing the validity of the proof. Without step 3, there would be a gap in the proof and it would not be considered complete.