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- Dictionarytrivial/ˈtrɪvɪəl/
adjective
- 1. of little value or importance: "huge fines were imposed for trivial offences" Similar Opposite
- 2. denoting a subgroup that either contains only the identity element or is identical with the given group.
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Nov 8, 2016 · Trivial solution is a technical term. For example, for the homogeneous linear equation $7x+3y-10z=0$ it might be a trivial affair to find/verify that $(1,1,1)$ is a solution. But the term trivial solution is reserved exclusively for for the solution consisting of zero values for all the variables. There are similar trivial things in other ...
$\begingroup$ Since the zero solution is the "obvious" solution, hence it is called a trivial solution. Any solution which has at least one component non-zero (thereby making it a non-obvious solution) is termed as a "non-trivial" solution. $\endgroup$ –
8. There are two meanings of the word "trivial" in mathematics. The first, as you rightly pointed out, is strictly defined and appears in most mathematical fields. By strictly defined, I mean that if you say "the trivial solution to the ODE y′ = g(x)y y ′ = g (x) y ", I know with certainty that you mean the solution y ≡ 0 y ≡ 0.
Oct 10, 2015 · A trivial solution is just only the zero solution and nothing more. In ordinary differential equations, when we way that we are looking for non-trivial solutions it just simply means any solution other than the zero solution. In your example, the trivial solution is. u(x) = 0, for all x in domain of interest u (x) = 0, for all x in domain of ...
Jul 31, 2017 · 1) Let a, b, c be not all 0. Then (0, 0, 0) is a trivial solution to the equation ax + by + cz = 0, because you can "see" it at once. 2) To prove that zz¯ = |z|2 for every complex z, the case where z = 0 is a trivial case. 3) The statement that every real number is a real number is a trivial statement.
Jul 1, 2019 · X = X is a trivial answer [more in the first part of my definition above] In applied mathematics using operations research [0,0,0] will often be a trivial answer because we would never want an instance of nothing happening.Yet mathematically [0,0,0] is possible. Getting an answer with a negative physical amount is often trivial. Such as a ...
Apr 5, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Jan 3, 2023 · In this light a trivial walk is neither open nor closed. We can say the set of closed walks for a graph G G is a subset of the set of nontrivial walks for G G. But many textbooks do define a closed walk simply as a walk with ending vertex equaling its starting vertex, so that a trivial walk is closed. I do not see a problem with this idea, and ...
Sep 18, 2019 · The link says, that a LTU can be represented when the expression is trivial and cannot be represented when it is non-trivial (page3). That's not what it says. First, you've mixed up what the role of LTUs is here.
Jul 9, 2011 · $\begingroup$ Please define your terms; this is hopelessly confusing. Some people use "Empty graph" to mean a graph with no edges that may still have nodes. You've said "the trivial graph" is the one with just one vertex, but it's not clear whether you're intending "empty graph" to mean the same thing as "trivial graph" in that sense. $\endgroup$
