Hardly. The construction method you cherish so requires a bijection. As has been pointed out many, many times before, the required bijection does not exist. This is a point that you continue to evade.
Since you are unable to address that point, perhaps you could simply describe, step by step, this construction method. So far, all you have shown are examples in which you don't follow any set rules for construction. Instead, you claim to generate what you started with. It continues to be a lame feat.
No, you didn't. You stepped through some examples without actually following any stated rules for construction.
This was your assertion. You did not, cannot prove it to be true. And there's no point you even trying until you actually lay out the rules you are following.
Except, you haven't shown a single bijection, yet. Not one. You claimed there were bijections for finite sets between the set and its power set. So, where are the bijections for {} and for {A}? You claimed there were bijections for infinite sets between the set and its power set. You bumbled through some arbitrary "rounds" then claimed you'd succeeded. Yet, there was no bijection to look at and no proof it was a bijection.
Irrelevant. You claimed bijections existed between the members of any set and its power set. Bijections between the whole numbers and the even whole numbers is trivial and unrelated to the problem before you.
When you manage to actually to demonstrate your own ability to express a complete, non-trivial reasoned thought, your criticism of others may then carry some weight.
[SIZE=+1]Again I ask: Can we expect to see your bijections between the elements of {} and its power set and the elements of {A} and its power set any time soon, or have you given up on this fool's errand?[/SIZE]
