# Beginning Sets: Advice on Set Building Notation?

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1. Nov 10, 2016

### Ryaners

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}

2. Nov 10, 2016

### PeroK

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 $n = -1, -2 \dots$.

3. Nov 10, 2016

### Ryaners

Thanks for the feedback!