Recursive order pairs

Posted on 2011-10-19
Last Modified: 2012-05-12
The following recursive definition defines a set Z or ordered pairs

B. (2,4) is in Z.
R1. If(x,y) is in Z with x < 10 and y <10, then (x+1, y+1) is in Z.
R2. If(x,y) is in Z with x > 1 and y < 10, then(x-1, y+1) is in Z.

Plot these ordered pairs in the xy-plane

I just did first line

B. (2,4) belongs to Z
Question by:mustish1
    LVL 13

    Expert Comment

    And what's stopping you from doing the next lines?  2 is less than 10 and greater than 1, and 4 is less than ten, so you have a couple obvious points right there, and another three in the generation after that, and so on.
    LVL 26

    Expert Comment

    I think you will wind up with 21 points.
    LVL 37

    Accepted Solution

    Draw a quick grid (I did it in Excel, but paper works fine). Mark point 2,4 and then look at the rules and keep marking all the points that fit and see what you get.

    I only got 19 points, by the way.

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