Is the set 7 5 3 well ordered prove or disproveSolutionA we

Is the set {-7, -5, -3, .....} well ordered?
prove or disprove.

Solution

A well-order on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the well-order relation is then called a well-ordered set.

Given set {-7,-5,-3,-1,1,3,...} is non empty sub set of real numbers and -7 is least element of S and its every non-empty subset has a least element.

Therefore it is a wellordered set.

Is the set {-7, -5, -3, .....} well ordered? prove or disprove.SolutionA well-order on a set S is a total order on S with the property that every non-empty subs

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