Definition:Strictly Increasing/Real Function

Definition

Let $f$ be a real function.

Then $f$ is strictly increasing if and only if:

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

Also known as

Some sources refer to this as an increasing real function, and use the term non-decreasing real function for what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called an increasing real function.

Some sources give it as a strictly monotonic increasing function

Also see

• Definition:Increasing Real Function
• Definition:Strictly Decreasing Real Function
• Definition:Strictly Monotone Real Function

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 12.1$
• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $1.7$: Terminology and Notation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): monotonic increasing function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): monotonic increasing function
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): increasing function