(February 14, 2018 at 1:28 pm)polymath257 Wrote:(February 14, 2018 at 1:10 pm)RoadRunner79 Wrote: So it would seem that an important part of if a complete set of infinite numbers is to define what it means to be a complete set? We didn’t do very well with defining a point, can we please define this. How is it complete, but not indicating a stop or an end?
It appears to me, that these sets are just loosely defined, or openly defined but how does that translate to the real world, and how can that be completed if it is open?
Well, to be complete means that we can tell exactly when something is in the list or not. For example, the number 1273749
is in the list 1,2,3,.... but the number 1.34 is not.
It is complete in the real world if everything in the list actually exists and we can tell exactly when something is in the list and when it is not.
I do believe that I was acting more on the second definition prevously. The first definition to me seems like you are saying a defined set, which seems pretty useless to me. If you cannot tell what is or is not in the set, then what good is it? In the end, I don't see that the involvement of sets (completed or otherwise) is really adding anything to the conversation. You can correct me if I'm wrong.
So to clarify what I am disputing is an actual infinite. Which would be completed or ended, on something which is unending. This is contradictory. You can not have an infinite. Even really in the abstract, you don't have an infinite number of things. You have a concept, which you think gives you an infinite number of things. But it's a never ending process (here there be dragons) which can never actualize infinity.
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If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther