Reciprocal Sequence is Strictly Decreasing/Proof 1

Theorem

The reciprocal sequence:

$\sequence {\operatorname {recip} }: \N_{>0} \to \R$: $n \mapsto \dfrac 1 n$

is strictly decreasing.

Proof

Follows from Reciprocal Function is Strictly Decreasing and from Restriction of Monotone Function is Monotone.

$\blacksquare$