A quarter of the way through the semester ALREADY. It always goes so fast.
Last week I got my first assignment for this course done. I didn't have a lot of difficulty with it.
I was impressed with myself with the way I solved question 4. Instead of combining the two related claims about binary strings, I proved only the claim about strings beginning and ending with the same bit. I accomplished this through my induction step. I went to the next string by inserting an arbitrary bit in the center (or Ceil(n/2)), thus preserving the same bit at each end. I thought this was clever.
I can see how one would prove this using the combined claim, but I wanted to see if my way would work and it did!
My plans for this week are to start the tutorial #2 problems. I have looked them over, I just haven't sat down to work them out. This is assuming my CSC209 assignment won't hog all my time. At least I got the assignment for this course finished so I'm not rushing on that.
On a side note, I wish my door didn't let in so much noise so I could still be asleep.
So long.
It is clever, and it uses Complete Induction (which is allowed for this question).
ReplyDeleteI had originally thought of the problem for Mathematical Induction, where the hint is most appropriate.
By the way, the insert idea will work for n>=2, but the claim is true for n=1 also.
I proved separately n=1 and n=2 as base cases.
DeleteOne other thing: be careful that you end up with strictly shorter binary strings when you use the induction hypothesis.
ReplyDeleteI'm not quite sure what you mean by this. I would think it would be implied, by adding a bit, that the previous string was strictly shorter.
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