(April 28, 2016 at 12:18 am)Excited Penguin Wrote:(April 27, 2016 at 12:34 pm)RoadRunner79 Wrote: I am confused by your statement, about the abstract of real numbers, not being infinite. Could you clarify? I do agree about the line though.... In any case you are going to have a finite number of points. You can redefine what the point means, but then you still have a finite number.
How exactly do you think that real numbers are infinite?
If you are talking about the abstract set including all real numbers, then it has no end. Any real number that you can think of; is in that set. You also do not have to reach any particular number by successive addition. All you have to do is verify that it meets the criteria of a real number.