Maximal, greatest, minimal and least elements of a set

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Maximal and greatest elements of a set refer to elements that are not exceeded by any other elements, while minimal and least elements are those that are not exceeded by any other elements in the set. In this discussion, element c is identified as a minimal element but not a least element, indicating the presence of another element that is not comparable to c. Elements d, i, e, f, and h are noted as not being comparable to c, highlighting the complexity of relationships within the set. Understanding these definitions is crucial for analyzing the structure of sets in mathematical contexts. The discussion emphasizes the importance of comparability in determining maximal and minimal elements.
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Definition of maximal, greatest, minimal and least elements of a set: http://i.stack.imgur.com/PnI9V.png

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Since c is a minimal element but c is not a least element, this implies that there is one element that is not comparable to c. What is that element? What about d and i?
 
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The elements ##d##, ##i##, ##e##, ##f## and ##h## are not comparable to ##c##.
 
If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and... then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those...

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