Synonymer & Information om | Engelska ordet TRIVIALLY

Exempel på hur man kan använda TRIVIALLY i en mening

• All polynomials: if a polynomial has degree n, any terms of degree larger than n in its Taylor series expansion must immediately vanish to 0, and so this series will be trivially convergent.
• For example, the El Gamal cryptosystem is semantically secure under chosen-plaintext attack, but this semantic security can be trivially defeated under a chosen-ciphertext attack.
• The main part of the proof will consider the case of a nonempty set, and examine the members in detail; in the case where the set is empty, the property is trivially possessed by all the members of the empty set, since there are none (see vacuous truth for more).
• For example, the flood fill algorithm is a simple but relatively robust algorithm that works for intricate geometries and can determine which part of the (target) area that is connected to a given (source) node in a multi-dimensional array, and is trivially generalized to arbitrary graph structures.
• Note that if the axiom of the empty set is not taken as a part of this system (since it can be derived from ZF + Infinity), then the empty domain also satisfies ZFC − Infinity + ¬Infinity, as all of its axioms are universally quantified, and thus trivially satisfied if no set exists.
• It won the 2001 8x8 Game Design Competition, even though the game was originally played on a 7x7 board, as it is trivially extensible to larger board sizes.
• The conjecture has been verified for a number of infinite classes of graphs (and, trivially, their complements).
• Note that the multiples of the identity act trivially on all flags, and so one can restrict attention to the special linear group SL(n,F) of matrices with determinant one, which is a semisimple algebraic group; the set of lower triangular matrices of determinant one is a Borel subgroup.
• Restricting to non-singular forms, one can do better than this: Heath-Brown proved that every non-singular cubic form over the rational numbers in at least 10 variables represents 0, thus trivially establishing the Hasse principle for this class of forms.
• This preordered set can in turn be considered as a category, which makes Ord a 2-category (the additional axioms of a 2-category trivially hold because any equation of parallel morphisms is true in a posetal category).
• It is important to note that most cryptographic techniques are trivially breakable if keys are not exchanged securely or, if they actually were so exchanged, if those keys become known in some other way— burglary or extortion, for instance.
• Coronene is produced in the petroleum-refining process of hydrocracking, where it can dimerize to a fifteen ring PAH, trivially named "dicoronylene".
• For one, the system used a simple pulse radar technique, which made it unable to detect targets close to the ground due to radar clutter as well as being trivially easy to jam using the recently-introduced carcinotron tube.
• Similarly if the frustum contains the entirety of the bounding volume, the contents may be trivially accepted without further tests.
• The "crude stereotypes" that Williamson refers to in the above passage are these: that analytic philosophers produce carefully argued and rigorous analyses of trivially small philosophic puzzles, while continental philosophers produce profound and substantial results but only by deducing them from broad philosophical systems which themselves lack supporting arguments or clarity in their expression.
• In full generality, the word link is essentially the same as the word knot – the context is that one has a submanifold M of a manifold N (considered to be trivially embedded) and a non-trivial embedding of M in N, non-trivial in the sense that the 2nd embedding is not isotopic to the 1st.
• Oded Goldreich and Leonid Levin (1989) showed how every one-way function can be trivially modified to obtain a one-way function that has a specific hard-core predicate.
• As such, it resembles the Dirichlet series for the polylogarithm, and, indeed, is trivially expressible in terms of the polylogarithm as.
• Anagram dictionaries were formerly produced by hand, but can now be trivially generated from any machine-readable word list by computer by sorting words in order of their sorted letter-strings.
• A player can either move one piece twice (this is the source of the famous trap in the "balanced" version of the game where White opening with pawn-two appears to be trivially busted by an unprincipled defense with the pawn on an adjacent file) or move two different pieces on their turn.

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