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| rdfs:comment | - Set theory is an obscure strain of mathematics. It is the study of things which may potentially contain other things. It is further theorized, through the principle of induction, that these contained things, in turn, may contain yet other things. Also, the contained things which are contained inside the previously mentioned contained things may yet contain other contained things that contain even more contained containers that may or may not reference themselves among other things. However, these things may not contain themselves, as that would just be plain silly.
- Sets are at the foundation of modern mathematics. However, many problems arise with the introduction of Axiomatic Set Theory. Not to put too fine a point on it, the following are examples. Does the set of all sets contain itself as a member? Consider the set S of all sets that aren't members of themselves. Is S a member of itself?
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| abstract | - Set theory is an obscure strain of mathematics. It is the study of things which may potentially contain other things. It is further theorized, through the principle of induction, that these contained things, in turn, may contain yet other things. Also, the contained things which are contained inside the previously mentioned contained things may yet contain other contained things that contain even more contained containers that may or may not reference themselves among other things. However, these things may not contain themselves, as that would just be plain silly.
- Sets are at the foundation of modern mathematics. However, many problems arise with the introduction of Axiomatic Set Theory. Not to put too fine a point on it, the following are examples. Does the set of all sets contain itself as a member? Consider the set S of all sets that aren't members of themselves. Is S a member of itself? And to confuse membership, consider all the things in a given refrigerator. Postulate the absence of pineapples. In some sense, the absence of pineapples is a presence in the refrigerator. If you're hungry for pineapples, you notice the absence of pineapples in the refrigerator. "No pineapples" are a presence in the set of things in the refrigerator. This is not simply the empty set. It is a way of distinguishing between different qualities of absence.
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