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- Triviality is used to describe a result that needs very less or no effort to prove or derive it. Its synonyms are unimportance, insignificance, in-consequence, etc. Richard Feynman, Nobel Prize winner, stated- “a trivial theorem is a theorem whose proof has been obtained once”.
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In mathematics, the term "trivial" is often used to refer to objects (e.g., groups, topological spaces) with a very simple structure. These include, among others: Empty set: the set containing no or null members; Trivial group: the mathematical group containing only the identity element; Trivial ring: a ring defined on a singleton set
A comprehensive collection of the most common symbols in probability and statistics, categorized by function into charts and tables along with each symbol's term, meaning and example.
Jan 20, 2012 · Power is the probability of correctly reject a false null hypothesis in a hypothetical situation where the data comes from a specific alternate hypothesis or range of alternates. Usually, this means "our statistical method should succeed" if "something is happening".
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- 50 useful statistics terms
Statistics is the analysis, interpretation and presentation of collected data. Statistical analysis is an important component of conducting effective research. Whether you’re a statistics student or use statistical language daily in your career, it can be helpful to understand and review the terminology you encounter in this branch of mathematics. ...
1. Alternative hypothesis
An alternative hypothesis is a theory that contradicts a null hypothesis. A null hypothesis is an informed assumption about whether your premise is true or if there’s any relationship between the two terms. If the data you collect demonstrates that your original hypothesis or the null hypothesis was correct, you can reject the alternative hypothesis. Related: Alternative Hypothesis: Definition and When To Use It
2. Analysis of covariance
Analysis of covariance is a tool for evaluating data sets that contain two variables: effect, which is referred to as the variate, and treatment, which is the categorical variable. The categorical variable emerges when one more variable, referred to as the covariate, arises. This analysis increases the accuracy of a study and removes possible bias.
3. Analysis of variance
An analysis of variance (ANOVA) compares the relationship between more than two factors to determine whether there’s a link between them.
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. The same goes for trivial subgroups, trivial topological spaces, trivial vector subspaces and so on.
Oct 25, 2024 · This module presents important terms that will be used throughout the text. This page titled 1.1: Definitions of Statistics and Key Terms is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.
Triviality Meaning in Maths. In Mathematics, triviality is a property of objects having simple structures. The word trivial is used for simple and evident concepts or things, such as – topological spaces and groups that have a simple arrangement. The antonym of trivial is non-trivial.
