And I explained why that’s not the case.
It can’t be in one-to-one correspondence because earlier statements say otherwise.
You stubbornly ignore the stated premises.
I will repeat myself one more time, just in case.
We started with the following situation:
Boy1 → Clone1
Boy2 → Clone2
Boy3 → Clone3
etc
We put the two sets in one-to-one correspondence. We paired every boy with exactly one clone and every clone with exactly one boy. This means that every boy is paired (which means there are no unpaired boys) and that every clone is paired (which means there are no unpaired clones.)
Once you remove Clone1 from the set of clones, you get the following situation:
Boy1
Boy2 → Clone2
Boy3 → Clone3
etc
Boy1 is now unpaired because we removed the clone he was paired with. At this point, there is no one-to-one correspondence between the two sets. In order to restore it, there must be a clone in the set of clones that is not paired – an unpaired clone. But there are NO unpaired clones. We STATED it earlier. And f there were unpaired clones, that would mean there was no one-to-one correspondence in the first place. But didn’t we put the two sets in one-to-one correspondence?
A possible way out is to say that by removing Clone1 a new clone is generated. But the problem with this is . . . that’s not what the word “remove” means. To remove a clone does not mean to remove a clone and add a new one.
Another possible way out is to say that there is no need for an unpaired clone to exist. You can just pair Boy1 with one of the paired clones. But the result of that wouldn’t be a one-to-one correspondence. You’d have a clone paired with TWO boys. One-to-one correspondence requires that every clone is paired with EXACTLY ONE boy.
How can you possibly argue against this?
You can’t.
The best you can do is redefine words to avoid admitting a mistake (on the part of mathematicians, that is, since people who post in this thread are merely following what mathematicians are doing.)