Restriction of Monotone Function is Monotone

Theorem

The restriction of a monotone mapping is monotone.

Proof

A restriction does not introduce any new arguments.

Hence the result follows trivially from the definition of monotone mapping.

$\blacksquare$

This article contains statements that are justified by handwavery. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding precise reasons why such statements hold. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Handwaving}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Also see

• Monotonicity of Real Sequences