The discussion revolves around the concept of comparing the cardinality of rational numbers within different intervals, specifically between [0,1] and [1,2]. Participants explore the implications of finding bijections between these domains and question the significance of such equivalences.
Participants generally agree on the method of using bijections to demonstrate the equivalence of the number of rational numbers in the specified intervals, though the significance of this equivalence remains a point of inquiry.
The discussion does not resolve the significance of the equivalence of the domains or the implications of these bijections beyond the mathematical demonstration of cardinality.
let me see if i understand, x is in [0,1] then f(x) is in [1,2] therefore f:x->f(x) therefore the number of rationals in [0,1] equals to [1,2].Originally posted by master_coda
To show that the number of rationals on [0,1] is the same as the number of rationals on [1,2] you just need to find a bijection from [0,1] to [1,2].
Clearly [itex]f(x)=x+1[/itex] is a suitable bijection.