In english based math language it seems that
non-increasing $\Longleftrightarrow$ less or equal (non-strict decreasing)
decreasing $\Longleftrightarrow$ strict less ( strict decreasing)
Is that correct ? If so, how does it make sense ?
I should note that even very good math teacher are making mistakes about this. Actually I asked this question after watching Boyd's video on convex optimization where even him is confused about this.... So I imagine many many people are, and there must be classes and tests about this absurd and buggy concept, which yields absolutely nothing interesting.
So I just wonder if I really am missing something, or if, yes, some people decided to create an abstraction that is leaky (not not increasing $\neq$ increasing ?) verbose (4 words, with special negation logic, instead of using the word 'strict' and keeping the usual well defined predicate logic rules)
absurdity of the concept
This notation is absurd for the following reason :
when dealing with element instead of functions we dont apply the same logic :
we dont phrase $x < y$ as "$x$ is less than $y$" nor "$x\leq y$" as "$x$ is not-more than $y$". (If we did though, at least it would not be so harmful as not not-more would mean more)
you have to define functions using a not notation, $f$ is non-increasing function $\Longrightarrow$ if $x$ is not-less than $y$, say 0.3 feet and 2.5 inches, then $f(x)$ is not-more than $f(y)$
This also violates a very basic tenet in programming style 101, which is here for a reason : never define or use something with a negation, it is confusing.
- To apply composition rules between functions, you better be buckled up with all the not. must be a fluff of cases
More profoundly, this violates a fundamental principle of logic which is that given some ambiguity, you should assume the most general case apply.
It is way worse than measuring things with non integral units. This is violating logical rules, and leaving a very basic concept obfuscated.