Beginning Sets: Advice on Set Building Notation?

[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}

Thanks in advance!

 

[PeroK]

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!

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

 

[Ryaners]

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

Thanks for the feedback!