ascending order

A sequence or arbitrary ordered set or one-dimensional array of numbers, $a$ , is said to be in ascending order if each $a_{i}\leq a_{i+1}$ . For example, the Fibonacci sequence is in ascending order: 1, 1, 2, 3, 5, 8, 13, 21 … The Perrin sequence is not in ascending order: 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17 …

In a trivial sense, the sequence of values of the sign function is in ascending order: … -1, -1, -1, 0, 1, 1, 1… When each $a_{i}<a_{i+1}$ in the sequence, set or array, then it can be said to be in strictly ascending order.

Title	ascending order
Canonical name	AscendingOrder
Date of creation	2013-03-22 16:06:39
Last modified on	2013-03-22 16:06:39
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	7
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 06A99
Related topic	DescendingOrder
Defines	strictly ascending order