Definition:Strictly Decreasing/Sequence

Definition

Let $\left({S, \preceq}\right)$ be a totally ordered set.

Then a sequence $\left \langle {a_k} \right \rangle_{k \in A}$ of terms of $S$ is strictly decreasing iff:

$\forall j, k \in A: j < k \implies a_k \prec a_j$

Real Sequences

The above definition for sequences is usually applied to real number sequences.

Let $\left \langle {x_n} \right \rangle$ be a sequence in $\R$.

Then $\left \langle {x_n} \right \rangle$ is strictly decreasing (or strictly order-reversing) if:

$\forall n \in \N: x_{n+1} < x_n$

Also see

• Decreasing Sequence
• Strictly Increasing Sequence
• Strictly Monotone Sequence

Sources

• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 4.15$