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In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
It is often argued that open-ended questions (i.e. questions that elicit more than a yes/no answers) are preferable because they open up discussion and enquiry. Peter Worley argues that this is a false assumption. This is based on Worley's central arguments that there are two different kinds of open and closed questions: grammatical and conceptual.
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous arguments or precise ideas. Much ...
Similarly, the slope of x+1/x is always less than 1, but the value of x+1/x is always greater than x (again, for x>0). The graph of y=√(x 2 +1) is one branch of a hyperbola having y=x as an asymptote, and this looks very much like the x>0 part of y=x+1/x.
The use of Unicode characters for blackboard bold is discouraged in English Wikipedia; instead, either the LaTeX rendering (for example <math>\mathbb{Z}</math> or <math>\Z</math>) or standard bold fonts should be used. As with all such choices, each article should be consistent with itself, and editors should not change articles from one choice ...
When it comes to asking for all solutions, it may be the case that conditions from mathematical analysis should be applied; for example, in the case of the Cauchy equation mentioned above, the solutions that are continuous functions are the 'reasonable' ones, while other solutions that are not likely to have practical application can be ...
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This allows using them in any area of mathematics, without having to recall their definition. For example, if one encounters R {\displaystyle \mathbb {R} } in combinatorics , one should immediately know that this denotes the real numbers , although combinatorics does not study the real numbers (but it uses them for many proofs).
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