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For some purposes, we also need this ideal to be a sigma-ideal, so that countable unions of negligible sets are also negligible. If I and J are both ideals of subsets of the same set X, then one may speak of I-negligible and J-negligible subsets. The opposite of a negligible set is a generic property, which has various forms.
Words for these concepts are sometimes cited as antonyms to schadenfreude, as each is the opposite in some way. There is no common English term for pleasure at another's happiness (i.e.; vicarious joy), though terms like 'celebrate', 'cheer', 'congratulate', 'applaud', 'rejoice' or 'kudos' often describe a shared or reciprocal form of pleasure.
In complexity-based modern cryptography, a security scheme is provably secure if the probability of security failure (e.g., inverting a one-way function, distinguishing cryptographically strong pseudorandom bits from truly random bits) is negligible in terms of the input = cryptographic key length .
As a result, air travels clockwise around high pressure in the Northern Hemisphere and anticlockwise in the Southern Hemisphere. Air around low-pressure rotates in the opposite direction, so that the Coriolis force is directed radially outward and nearly balances an inwardly radial pressure gradient. [38] [better source needed]
"Unpaired words" at World Wide Words "Absent antonyms" at 2Wheels: The Return; Words with no opposite equivalent, posted by James Briggs on April 2, 2003, at The Phrase Finder; Brev Is the Soul of Wit, Ben Schott, The New York Times, April 19, 2010; Parker, J. H. "The Mystery of The Vanished Positive" in Daily Mail, Annual for Boys and Girls ...
Two words: Apple Intelligence. The latest iOS 18.2 with new Apple Intelligence features may have underwhelmed thus far (Genmoji and Image Playgrounds alongside ChatGPT are fine additions, but ...
The third book in the Yarros’ “Empyrean” series comes out in January from Entangled Publishing. The follow-up to “Fourth Wing” and “Iron Flame” swaps Basgiath War College lessons for ...
Complementary antonyms are word pairs whose meanings are opposite but whose meanings do not lie on a continuous spectrum (push, pull). Relational antonyms are word pairs where opposite makes sense only in the context of the relationship between the two meanings (teacher, pupil). These more restricted meanings may not apply in all scholarly ...