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A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
Consider the formal sentence . For some natural number , =.. This is a single statement using existential quantification. It is roughly analogous to the informal sentence "Either =, or =, or =, or... and so on," but more precise, because it doesn't need us to infer the meaning of the phrase "and so on."
The Unicode Standard encodes almost all standard characters used in mathematics. [1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. [1]
Mathematics finds a place in science only as one of the symbolical languages in which scientific explanations may be expressed." [ 25 ] These definitions tend to emphasize the subject matter of science rather than its method and from these perspectives, the philosophical concern to establish a demarcation between science and non-science becomes ...
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in "discrete" steps and ...