And what you are counting has nothing to do with its countability. The boards may be 6 inches wide or they may be 4 feet wide (that's the width of a sheet of plywood in the US). But as long as all I am interested in is counting them it doesn't matter.
Correct I already told you that ... if you can't see anything but the boards or don't consider anything but the boards I gave the same answer ... go back and read
Surely you see the problem if there is an outside world here let me write it mathematically for the two situations
Exact board formula:
Real world distance of boards = number of boards x 6 inches
Inexact Board formula:
Real world distance of boards = number of boards x (6 inches +- uncertainty)
The first case holds for each and every value including infinity whether a number or concept. Now try doing it in the second case you can't even do a finite much less infinity.
The problem is there are actually two infinities (one in the world and one in the boards) and regardless of whether you consider infinity to be a concept or a number they are supposed to imply and match the same definition. They don't in the second example so it is hard to work out what to do other than saying it's undefined without more information.
The question is: IS INFINITY A NUMBER?
You set that answer in your selection of basis of countable numbers and that system says infinity as not a number.
The answer is: INFINITY IS NOT A NUMBER!
Your answer is correct but it is merely reflecting back the selection you made in selecting countable numbers.
So your answers are correct to the number basis you selected and I completely agree with you and the logic. The bigger problem is the are hundreds possibly thousands of other number basis you could have used that give very different answers that are equally correct.
So the real question to consider is does your number basis represent a good fit to the physics in the real world because that is what Bill S is trying to work with infinity in the start post?
If you are happy that it is the best fit then your answer makes perfect sense to me and I have listened to you.
