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In this section, we use a similar technique to solve the sorting problem, that is, starting with an unordered array of elements and rearranging them into non-decreasing order.

This line is taken from a coding textbook where they are basically discussing sorting algorithms. Sorting algorithms either sort in an increasing order or a decreasing order depending on the input type.

Does the word non-decreasing here mean same as that of increasing? Is there any particular situation where they have different meanings? Also, can these two words be used interchangeably in a context?

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  • The answer given is correct. However, there is no doubt that a lot of the time (certainly in less technical speech) "increasing order" means the same thing as "non-decreasing order". If someone asked me to sort 1, 2, 3, 4, 4 into increasing order, I would simply sort them into non-decreasing order. I wouldn't say "oh, no, that's impossible".
    – rjpond
    Commented Sep 21, 2020 at 6:31

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No, the difference is behavior at the limit.

  • Non-decreasing includes both increasing and level ordering; e.g., 1, 2, 3, 3, 4.
  • Increasing excludes steady-state, so in the previous example, "3, 3" is not allowed.

Compare with similar math operators, greater-than (>) vs. greater=than-or-equal-to (>=).

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