Just another light-hearted and trivial thread, namely a question, on whether distinct (to be defined later) mathematical notions have to be of finite number.
By distinct i mean notions which can (according to any, yet logical and clear, categorization) be argued to be sufficiently different and non-dependent on each other. For example one could argue that the notion of group is sufficiently distinct from the notion of integer, while ultimately both are dependent on the notion of oneness.
My suspicion is that they do not have to be finite, provided that the group of core notions by which they are tied is sufficiently large. Also it should be noted that with new formation of notions more types of dependency are identified, thus enriching the group of "core" notions.
I also suspect that the number of different categorization methods also do not have to be finite, due to the same - trivially variated- reason.
tldr: when one is too lazy to read on incompleteness of set theory, by not too lazy to post on a web forum.
By distinct i mean notions which can (according to any, yet logical and clear, categorization) be argued to be sufficiently different and non-dependent on each other. For example one could argue that the notion of group is sufficiently distinct from the notion of integer, while ultimately both are dependent on the notion of oneness.
My suspicion is that they do not have to be finite, provided that the group of core notions by which they are tied is sufficiently large. Also it should be noted that with new formation of notions more types of dependency are identified, thus enriching the group of "core" notions.
I also suspect that the number of different categorization methods also do not have to be finite, due to the same - trivially variated- reason.
tldr: when one is too lazy to read on incompleteness of set theory, by not too lazy to post on a web forum.
