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Beginning Sets: Advice on Set Building Notation?

  1. Nov 10, 2016 #1
    I've started Book of Proof, the first chapter of which is an intro to sets.

    Q.1
    Is there any particular way to approach these kinds of problems, other than using intuition / trial & error? I tend to have some difficulty in working out the best way to express the general term of a sequence, for example (which is essentially the same thing as using set-building notation, as far as I can tell..?). Maybe it's just a practice game - any pointers welcome nonetheless!

    Q.2 In the solutions to exercises on set building notation in the book, the letters n, k and x are all used in different cases - is there an established 'good practice' as to which should be used in a given situation, or is consistency within a given problem all that matters?

    Q.3
    I'd like to check if I've done this particular one right:
    The exercise:
    Write the following set in set-builder notation: {... , -8, -3, 2, 7, 12, 17, ...}
    What I've got:
    {(5n+2) : n ∈ ℤ}

    Thanks in advance!
     
  2. jcsd
  3. Nov 10, 2016 #2

    PeroK

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    Q1 It's just practice and generally grasping the concept of what you are doing.

    Q2. Usually ##i, j, k, l, m, n## are used for integers and ##x, y, z## for real numbers. But, as long as you make clear what the symbols mean, consistency is key.

    Q3. Yes, that's right. You could check it yourself just put putting ##n = 0, 1, 2 \dots## then ##n = -1, -2 \dots##.
     
  4. Nov 10, 2016 #3
    Thanks for the feedback!
     
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