Example:
Is the sequence 
monotone increasing or decreasing ?
We will not attempt to guess what the correct answer might be.
We will instead simply look at the difference between two
consecutive terms and see if that comes out greater or
less than zero.
This means that the n-th term minus the (n+1)-th
term of the sequence is less than 0, so that the n-th
term is less than then (n+1)-th term.
That means, by definition, that the sequence is increasing.
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