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An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: [1] The student of arithmetic who has mastered the first four rules of his art and successfully striven with sums and fractions finds himself confronted by an unbroken expanse of questions known as problems ...
Sections 10, 11, 12: Properties of a variable extended to all individuals: section 10 introduces the notion of "a property" of a "variable". PM gives the example: φ is a function that indicates "is a Greek", and ψ indicates "is a man", and χ indicates "is a mortal" these functions then apply to a variable x .
The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
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 ...
Rule 110 - most questions involving "can property X appear later" are undecidable. The problem of determining whether a quantum mechanical system has a spectral gap. [9] [10] Finding the capacity of an information-stable finite state machine channel. [11] In network coding, determining whether a network is solvable. [12] [13]
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations.
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