Hi all,
I think I have figured out what I will do for the mathematical problem I need to solve on this slog.
My idea is: to prove that a number is a multiple of 11 if starting from the right you take the first digit, then subtract the second digit, then add the third digit, then subtract the next and so forth; then if that number is a multiple of 11 (positive, negative or zero) then the original number is also a multiple of 11.
I think this might be able to be proved using complete induction. I see a few problems arising. One is proving that the number I get in the add subtract step is smaller than the previous number always (although I think I sorta see how to prove that). Another is how to prove that if the new number is a multiple of 11 the previous one is also. After that it could be fairly straight forward. I guess part of it will be seeing it in action with numbers where the add subtract step gets a number >= 11.
By the way I got this algorithm from http://www.counton.org/explorer/primes/divisibility-tests-for-9-and-11/
So long for now.
Showing posts with label induction. Show all posts
Showing posts with label induction. Show all posts
Thursday, 18 October 2012
Monday, 1 October 2012
Week 4 Begins
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.
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.
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