Order of a set

[eranga262154]

Hi,

Let say I have a set of positive whole numbers which satisfied the inequality 8 < X. So the set of values should be 7,6,5,4,3,2,1. The exact way to represent that set is {….,4,5,6,7} or {7,6,5,4,….}. I mean the order of the set is important.

[krtxmrtz]

Hi,

Let say I have a set of positive whole numbers which satisfied the inequality 8 < X. So the set of values should be 7,6,5,4,3,2,1. The exact way to represent that set is {….,4,5,6,7} or {7,6,5,4,….}. I mean the order of the set is important.

If X represents the members of the set and 8<X then all members are larger than 8, i.e. the set would be {9,10,11,...}

And your sentence above "The exact way..." is a question or a statement?

[yrwyddfa]

A set, in the strictest terms, is unordered. If it was ordered then it becomes a sequence.

eg:the set {1,2,3} is identical to {3,1,2} and {3,2,1}

However the sequence <1,3,2> is not the same as <3,1,2> nor <3,2,1>

More formally the sequence is properly defined as the set {(1,1),(2,3),(3,2)} (which is a sequence of pairs) where the first element of each subset determines order, but is normally abbreviated (as above) to <1,3,2> where natural left-right ordering is implied.

Another property of sequences is that duplication is allowed. For instance {1,2,2,3} is not a valid set, but <1,2,2,3> is a valid sequence. A sequence also does not need to comply with any natural ordering, so <3,2,1,2> is a valid sequence but it is not the same as <1,2,2,3>

Hope this helps,

Mark

[eranga262154]

If X represents the members of the set and 8<X then all members are larger than 8, i.e. the set would be {9,10,11,...}

And your sentence above "The exact way..." is a question or a statement?

Sorry about that mistake. It should be 8 > X.

And I mean "The exact way..." is that which one is the correct.

[eranga262154]

Hope this helps,

Fine replay

Thanks