What are the 3 methods in writing sets?

Answer 1

1. For finite sets, and some sets with no pattern you can write down the elements.

{a1, a2, a3, a4, ....., an} or {a1, a2, a3, ....} for infinite sets

e.g. {1, 3, 5, pi/sqrt(2)}

{1, 2, pi, 56, 4, i, sqrt(pi), ...}

You can do this with all sets, there is no order required.

2. If there is a generic way of describing the set, as in there is one universal pattern for all of them then you can write:

{x | x satisfies P(x)} where P is a condition

2'. For sets have a name and a symbol, for instance the natural numbers, just write the symbol.

bolded N for natural numbers

3. If a set is countable, meaning its elements can be written in a sequence an (a sequence is an infinite order of "numbers" with respect to the natural numbers) then you can write:

{an} to represent the set.

e.g. (an) = ((-1)^n) = (-1, 1, -1, 1, -1, 1, -1, ...).

Then we can say {an} = {(-1)^n} but there are only two distinct elements, so it's also {1, -1}

A better one. (bn) = (1/2^n) = (1/2, 1/4, 1/8, 1/16, ....)

Write {1/2^n} suffices.

Note: You have to specify that n is a natural number beforehand so both the sequence and set notation makes sense

Can't think of a fourth way yet.