Here is a newsflash there is nothing in the world that has an exact measurement and this is part of the problem I am trying to get Bill S to understand. When a layman says 6 inches there is some inaccuracy that is allowed which is obviously dependant on the application. A 6 inch piece of lumber is probably something like a range 5.95 to 6.05 inches which a layman calls 6 inches because that is as close as he needs to know.
Once again that is questionable. It depends on what you are referring to. For instance a 1 by 6 piece of lumber is nominally 1" thick by 6" wide. In fact it is 0.75" by 5.75". That is the finished dimension of a board that was originally cut to be 1X6.
But you are still evading Bill's question. Whether any measurement can be exact has nothing to do with the question of whether infinity is a number. You can have an infinite number of 6" boards that are exactly 6", or you can have an infinite number of 6" boards where the measurement is inexact.
In my opinion, without doing any deep philosophical thinking, infinity is not a number. George Gamow wrote a book titled "One, Two, Three, Infinity". He discussed the matter of primitive tribes having only a limited quantity of counting numbers. To me infinity just means more than I can count, the same as those primitive tribes. And for that there is no reference to the counting system used. In modern mathematics infinity means more than I can count in principle. There may be some numbering systems which are circular and you reach a point where numbers start repeating or decreasing. I don't know if there are any such, but mathematics being what it is I don't want to throw the idea out. Aside from any such systems, in principle, if you name a numbering system and give me a number of any size I can always add one more to that. But if I look at a series and can see that this is possible I just say the series goes to infinity. So infinity is more of a description than it is a number.
At the same time I don't see this as being something that precludes anything, such as the universe, being infinite in size. And being infinite in size just means that there is no way, even in principle, to measure it. That means that we don't say it is infinite just because we don't see a way to measure it, but that we cannot even imagine any way for it to be measured by ignoring physical reality.
And of course I have no idea whether the universe is infinite. It may be or it may not be.
Bill Gill
