The term actual infinity is contradictory.
Infinite of course refers to limitless or endless. It cannot be ended, or completed. It cannot be contained or actualized in it's entirety or limited. Therefore when you put the two together, it is a contradiction.
Infinity means that there is no limit, that there is always something more. You cannot bind it and say "here is infinity" at any given point. You will have a potential infinity, which may be increased.
Quote:The mathematical meaning of the term "actual" in actual infinity is synonymous with definite, completed, extended or existential, but not to be mistaken for physically existing. [ wiki ]
Infinite of course refers to limitless or endless. It cannot be ended, or completed. It cannot be contained or actualized in it's entirety or limited. Therefore when you put the two together, it is a contradiction.
Quote:Infinity turns out to be the opposite of what people say it is. It is not 'that which has nothing beyond itself' that is infinite, but 'that which always has something beyond itself'. (Aristotle)
Infinity means that there is no limit, that there is always something more. You cannot bind it and say "here is infinity" at any given point. You will have a potential infinity, which may be increased.
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. - Alexander Vilenkin
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther
