Definition:Decreasing/Real Function

Definition

This definition continues to hold when $S = T = \R$.

Thus, let $f$ be a real function.

Then $f$ is decreasing iff:

$x \le y \implies f \left({y}\right) \le f \left({x}\right)$.

Also see

• Strictly Decreasing Function
• Increasing Function
• Monotone Function

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $12.8$
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 12.1$