Many of these notions of infinity simply add resolution to other notions of infinity. In the finites, what counts as a distinct number is generally clear (except for the infintesimals), but for the infinites, sometimes it is convenient to merge what could be considered distinct numbers togethers. For example, since there is a bijection from X to X+1, and hence from X to X+n, for any finite n, we are tempted to treat all these entities as the same as we really can’t distinguish them very well. Unfortunately, some people conflate an inability to distinguish elements as the seperate elements not having their own existence, but it is well known, for example, that there are numbers that exist, but which can’t be explicitly described and no-one says that these elements are all the “one” element.
Many of these notions of infinity simply add resolution to other notions of infinity. In the finites, what counts as a distinct number is generally clear (except for the infintesimals), but for the infinites, sometimes it is convenient to merge what could be considered distinct numbers togethers. For example, since there is a bijection from X to X+1, and hence from X to X+n, for any finite n, we are tempted to treat all these entities as the same as we really can’t distinguish them very well. Unfortunately, some people conflate an inability to distinguish elements as the seperate elements not having their own existence, but it is well known, for example, that there are numbers that exist, but which can’t be explicitly described and no-one says that these elements are all the “one” element.