weakly increasing function
nounUK /ˈwiːkli ɪnˈkriːsɪŋ ˈfʌŋkʃən/
US /ˈwiːkli ɪnˈkriːsɪŋ ˈfʌŋkʃən/
A function that never goes down as you move to the right.
The step function is weakly increasing because it stays flat and then jumps up.
SYNONYMS
OTHER MEANINGS
2. A function f where x ≤ y always implies f(x) ≤ f(y).
On the real line, f(x) = x² is not weakly increasing over all reals, but it is on [0, ∞).
3. A map between posets that preserves the order relation in one direction.
Every weakly increasing function from a poset to itself is order-preserving.
4. A sequence whose terms never decrease from one index to the next.
The sequence 1, 1, 2, 2, 3 is weakly increasing.