The difference between Nonpositive and Nonvanishing
When used as adjectives, nonpositive means not positive, whereas nonvanishing means (of a quantity) that is nonzero at all points in a space.
Nonpositive is also noun with the meaning: any value that is not positive.
check bellow for the other definitions of Nonpositive and Nonvanishing
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Nonpositive as an adjective (mathematics, of a quantity):
Not positive; either zero or negative.
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Nonpositive as a noun:
Any value that is not positive.
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Nonvanishing as an adjective (mathematics):
(of a quantity) that is nonzero at all points in a space