The discussion revolves around the properties of infinite subsets of the real numbers, particularly focusing on the relationship between the number of terms in a set and its length. Participants explore whether an infinite subset necessarily implies an infinite length or if it can have a finite length despite containing infinitely many elements.
The discussion is active, with participants providing examples and counterexamples to clarify their points. Some guidance has been offered regarding the nature of infinite sets, but no consensus has been reached on the implications of these properties.
There is an ongoing exploration of definitions related to length and terms in infinite sets, with references to specific examples that challenge initial assumptions. The conversation reflects a mix of perspectives on the topic.
No.jason177 said:Alright this is a pretty simple question. So if A is a infinite subset of the reals, does that mean that its length is infinite (eg. the set of all numbers from 0 to infinite)
Yes.In fact its length could be zero.or could it also be just a set with an infinite number of terms (eg. the set of all real numbers between 1 and 2)?
jason177 said:Alright this is a pretty simple question. So if A is a infinite subset of the reals, does that mean that its length is infinite (eg. the set of all numbers from 0 to infinite) or could it also be just a set with an infinite number of terms (eg. the set of all real numbers between 1 and 2)?