Scheme is great. I wouldn't actually use it, though, with all the politics and bullshit going on. At least Common Lisp was practically set in stone in 1994, and lets people to go on with simply hating the standard while providing useful solutions to fix it.
The intuition behind the formal definition of cardinal is the construction of a notion of the relative size or "bigness" of a set without reference to the kind of members which it has. For finite sets this is easy; one simply counts the number of elements a set has. In order to compare the sizes of larger sets, it is necessary to appeal to more subtle notions.
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Anonymous2013-09-01 16:03
The above systems can be modified to allow urelements, objects that can be members of sets but that are not themselves sets and do not have any members.