Everyone knows a sequence when they see one. People standing in a queue form a sequence. A list of tasks that someone writes out to plan their day is also a sequence.

A sequence is an arrangement of objects, people, tasks, grocery items, books, movies, or numbers, which has an ‘order’ associated with it. To have an order associated with it, it must be in correspondence with the set of natural numbers. More rigorously, a sequence is a function from the set of natural numbers to any given set. This set may be finite or infinite. And although elements may not be repeated in a set, they may be repeated in a sequence.

The set of natural numbers itself forms a sequence. 1, 2, 3, 4, 5… is a sequence. So is 1, 1, 2, 2, 3, 3…, even though the numbers are repeating.

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