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When comparing numbers to zero, the phrases "strictly positive" and "strictly negative" mean "positive and not equal to zero" and "negative and not equal to zero", respectively. In the context of functions, the adverb "strictly" is used to modify the terms "monotonic", "increasing", and "decreasing".
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On the other hand, sometimes one wants to specify the inclusive meanings of terms. In the context of comparisons, one can use the phrases "non-negative", "non-positive", "non-increasing", and "non-decreasing" to make it clear that the inclusive sense of the terms is being used.
50:, which is often understood to be the case but can be put explicitly for clarity. In some contexts, the word "proper" can also be used as a mathematical synonym for "strict".
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The use of such terms and phrases helps avoid possible ambiguity and confusion. For instance, when reading the phrase "
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refers to the property of excluding equality and equivalence and often occurs in the context of
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The word "proper" is often used in the same way as "strict". For example, a "
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is not less than zero. Such an ambiguity can be mitigated by writing "
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