A better way to frame it is that the example treated the two hydrogen atoms in H-O-H as the same thing, when in fact they are not, in the same way that there are three fruits in a collection with 2 apples and 1 orange, not two, because the two apples aren’t the same thing. You can say that the set of atoms in H-O-H is {the first H, the second H, the O}
...except, you can’t? On a quantum mechanical level, two hydrogens don’t have XML tags labelling which one they are. This is easier to explain with electrons. You cannot say that the first electron is here, and the second there.
A better way to frame it is that the example treated the two hydrogen atoms in H-O-H as the same thing, when in fact they are not, in the same way that there are three fruits in a collection with 2 apples and 1 orange, not two, because the two apples aren’t the same thing. You can say that the set of atoms in H-O-H is {the first H, the second H, the O}
...except, you can’t? On a quantum mechanical level, two hydrogens don’t have XML tags labelling which one they are. This is easier to explain with electrons. You cannot say that the first electron is here, and the second there.