Your reasoning still lies in the fallacy that I discovered.

This is what you say:

1. If X is an actual world then X is a possible world.

2. If X is a possible world then X is an actual world.

Consider now the following statement (contrapositive of 2)

3. If X is not an actual world then X is not a possible world (contrapositive of 2)

3. If X is not an actual world then X is not a possible world.

Undoing what we did, we get

4. If X is a possible world then X is an actual world (contrapositive of 3). This statement is true.

If X is an actual world (if apple is a fruit) then it is a possible world (a possible fruit) See how this argument is beginning to fall apart? You're stating that something real is a possibility of being real. This is a logical contradiction. Moving on.

If X is a possible world (a possible fruit) then X is an actual world (an actual fruit)

Still this doesn't make sense because as I said, the set of all possible conditions must be greater than the set of all actual objects. This is because a set of possible X should mean there is number of X that is not actual. The set of possible worlds therefore is greater than the set of actual worlds.

Therefore, we cannot say your second point as it is a logical contradiction. If X is a possible world it does not mean that X is an actual world because the set of X as possible worlds is bigger than the latter. Moving on.

You say in point 3 that if X is not an actual world then X is not a possible world. This contradictions everything you've said and been building up to so far. I can imagine a world that is made of gas, and although this planet is not real, it can be a possible world because it contains all the conditions of being real. For example, if something has possible properties then it is possible but not always actual.

Going to point 4 now which is built upon several logical mishaps, we will see that the conclusion must be false or at least doubtable. This can be done simply however.

Fourth point: If X is a possible world then X is an actual world. You just said in point 3 that if X is not an actual world then X is not a possible world. This is a complete contradiction to each other.

According to what you said, the set containing all possible worlds is equivalent to the set of all actual worlds. First of all "possible" means that there is a possibility that the world in question is not actual. This means that the set of possible worlds can never equal the set of actual worlds, because actual worlds are manifestations of conditions whereas possibility itself is a condition to be questioned. Therefore possibility is always superior in its set than actual manifestations of it, otherwise there is no need to use the word "possibility"- merely just call it actual- but before actuality there is always possibility and therefore the two cannot be equated to each other as you have done.

Also this is what you're saying.

1. If X is an actual world then X is a possible world.
2. If X is a possible world then X is an actual world.

I can also say:

1. If is apple then it is a fruit
2. If is fruit then it is an apple

Possible world has a greater scope that contains all actual worlds
Therefore you can't say that a possible world is an actual world because possible worlds do not completely contain actual worlds in its set- there are some worlds that are just potential. Otherwise it would be not be a set of potential worlds but actual worlds.

Possible worlds are only relevant when it comes to propositions. The possible worlds make up for the sense ingredient for each separate reference. It does not point at the truth at all. For example, there is a world where snow is blue but in this world snow is white, so we get a sense of "white" when we mention snow because in this world snow is white.

Therefore possible worlds are needed as a way for us to make sense of what is NOT. It has no value when it comes to proving something that may exist in our world.