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Cutting a string at 'n' positions in any order will yield same cut pieces. Is there any standard mathematical proof which supports this ?

For example say "elephantsinforest" is the string.

Cutting the string at id cut positions in increasing order (5,9,12) yields {eleph, ants, inf, orest} chunks.

If we consider string id cut positions in a random order (9, 5, 12) yields {eleph, ants, inf, orest} chunks.

If we consider string id cut positions in decreasing order (12, 9, 5) yields {eleph, ants, inf, orest} chunks.

So whatever the cut id position ordering, we ultimately end up with same set of cut string chunks. How can we prove this mathematically? Can any one suggest how to prove this mathematically or are there any standard exisiting proofs for the given context ?

ganapathi
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  • can anyone suggest relevant tags for this question ? – ganapathi Sep 13 '16 at 09:55
  • @ChristianBlatter thanks for the reply. Yes, the ordering of cuts has no role as in whatever order you cut the string ...finally yields the same set of cut chunks. As the position of cut is independent of ordering. How can we prove this ? – ganapathi Sep 14 '16 at 04:03
  • I don't think there is anything to prove. The resulting list of chunks is determined by the set of chosen cuts. This set does not depend on the order its elements are listed. – Christian Blatter Sep 14 '16 at 07:27
  • @ChristianBlatter Yeah! got it but is there is any standard problem which sstates the same thing whever you mark on a string ...random cut positions will yield same result. It will be very helpful if some standard problem model states the same thing – ganapathi Sep 18 '16 at 09:44

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