Set Builder Notation?

Let's break it down.

A is the name of the set which is equal to a set which you are then going to "build".

A = { ... }

The set consists of elements (x) with the following characteristics.

A = {x : .... }

The first characteristic is that x is between 3 and 5 inclusive.

We could write that as:

x ≥ 3 and x ≤ 5

As you noted, it then uses the ≥ symbol to say that x is greater than or equal to 3. But then we go a step further and make it into a compound statement. We turn the first statement around:

3 ≤ x (in other words, if x is greater than or equal to 3, we could say 3 is less than or equal to x).

3 ≤ x and x ≤ 5

But we don't need to repeat x and use the 'and'. We can create a compound inequality with a single subject x in the middle:

3 ≤ x ≤ 5

The last part is just saying that x is also an element of the natural numbers, so that would exclude numbers like π, 4½ or 4.75 as being included.

A = {x : 3 ≤ x ≤ 5, x ∈ N}

Answer:

The inequality symbol always points from the bigger element to the smaller element. We want to show that 3 is smaller (or equal) than x, so when x is on the right, the symbol points toward the smaller value (3) on the left.

Okay so inequalities work like this

x ≥ 3

x ≤ 5

Means

3 ≤ x

x ≤ 5

So put together

3 ≤ x and x ≤ 5

3 ≤ x ≤ 5