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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 ...
An antonym is one of a pair of words with opposite meanings. Each word in the pair is the antithesis of the other. A word may have more than one antonym. There are three categories of antonyms identified by the nature of the relationship between the opposed meanings.
In printed mathematics, the norm is to set variables and constants in an italic typeface. [ 17 ] For example, a general quadratic function is conventionally written as a x 2 + b x + c {\textstyle ax^{2}+bx+c\,} , where a , b and c are parameters (also called constants , because they are constant functions ), while x is the variable of the function.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination—for example, = leaves open what the value of is—while overdetermination, except when like =, =, =, is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system ...
Mathematics has a remarkable ability to cross cultural boundaries and time periods. As a human activity, the practice of mathematics has a social side, which includes education, careers, recognition, popularization, and so on. In education, mathematics is a core part of the curriculum and forms an important element of the STEM academic disciplines.
One common understanding of formalism takes mathematics as not a body of propositions representing an abstract piece of reality but much more akin to a game, bringing with it no more ontological commitment of objects or properties than playing ludo or chess. In this view, mathematics is about the consistency of formal systems rather than the ...
We have in the latter part of the above paragraph referred to the philosophical importance of the antinomies of reason, and shown how the recognition of their existence helped largely to get rid of the rigid dogmatism of the metaphysic of understanding, and to direct attention to the Dialectical movement of thought. But here too Kant, as we ...