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Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous arguments or precise ideas. Much of this uses common English words, but with a specific non-obvious meaning when used in a mathematical sense. Some phrases, like "in general", appear below in more than one section.
An event defines a complementary event, namely the complementary set (the event not occurring), and together these define a Bernoulli trial: did the event occur or not? Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as events). [5]
The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc.) with concision, precision and unambiguity.
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
For example, "odds of a weekend are 2 to 5", while "chances of a weekend are 2 in 7". In casual use, the words odds and chances (or chance) are often used interchangeably to vaguely indicate some measure of odds or probability, though the intended meaning can be deduced by noting whether the preposition between the two numbers is to or in. [5 ...
An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
A geometry: it is equipped with a metric and is flat. A topology: there is a notion of open sets. There are interfaces among these: Its order and, independently, its metric structure induce its topology. Its order and algebraic structure make it into an ordered field.
For example, a glass breaking on the floor is an event; it occurs at a unique place and a unique time. [1] Strictly speaking, the notion of an event is an idealization , in the sense that it specifies a definite time and place, whereas any actual event is bound to have a finite extent, both in time and in space.