Descending Order
Descending order means arranging numbers from largest to smallest.
Formula
a_1 \ge a_2 \ge a_3 \ge \ldots
Definition
Descending order means arranging numbers from largest to smallest, going down. Formally, a sequence is in descending (non-increasing) order if each term is less than or equal to the previous, $a_1 \ge a_2 \ge \ldots \ge a_n$, or strictly descending if each term is strictly less. This corresponds to the reverse total order, and a bounded descending sequence of real numbers converges by the monotone convergence theorem (viewed as a bounded ascending sequence under the reverse order); standard polynomial convention writes terms in descending order of degree, as in $3x^4 - 2x^2 + x - 5$.
Example
$50, 35, 18, 9, 2$ are in descending order, each number smaller than the one before. Arrange in descending order: $0.5, -2, 3, 1/4, -0.1$ converts to decimals as $3, 0.5, 0.25, -0.1, -2$. The sequence $1/n$ is strictly descending and bounded below by $0$, converging to $0$, while $2, 3/2, 4/3, 5/4, \ldots = 1 + 1/n$ is descending and converges to $1$.
Key Insight
"Descending" means "going down," like walking downstairs, each number smaller as you move along. Descending order is often used for rankings and for counting down, and any ascending list reversed becomes descending. Polynomials written in descending degree order make the leading term and degree immediately visible, important for division, asymptotic analysis, and evaluation by Horner's method.