-=Dark_Angel=-, P.I.26 Mar 2005

No.

I did not say the valves are "of the same kind." That's something you just invented.

Stop imagining that I am talking about a single valve, or a single type of valve, that is identical open and closed. That seems to be the main source of your confusion.

I am simply saying that there is a one-to-one correspondence between two sets. You can't seem to fit that into your head. Do you know what a one-to-one correspondence is?

Think about the set of positive numbers, and the set of negative numbers. For every positive number, there is a negative number with the same absoulte value. For every negative number, there is a positive number with the same absolute value. Therefore there is a one-to-one correspondence between the two sets.

Do you accept that there is a one-to-one correspondence between the set of all possible open valves and the set of all possible closed valves?