Definition:Increasing/Real Function

Definition

Let $f$ be a real function.

Then $f$ is increasing iff:

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

Also see

• Strictly Increasing Function
• Decreasing Function
• Monotone Function

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $12.8$
• A.N. Kolmogorov and S.V. Fomin‎: Introductory Real Analysis (1968): $\S 3.2$
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 12.1$