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Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [ 1][ 2][ 3] also known as De Morgan's theorem, [ 4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British ...
Stokes' theorem, [ 1] also known as the Kelvin–Stokes theorem[ 2][ 3] after Lord Kelvin and George Stokes, the fundamental theorem for curls or simply the curl theorem, [ 4] is a theorem in vector calculus on . Given a vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the ...
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product is a product distribution .
The doctrine of necessity is the basis on which extraordinary actions by administrative authority, which are designed to restore order or uphold fundamental constitutional principles, are considered to be lawful even if such an action contravenes established constitution, laws, norms, or conventions. The maxim on which the doctrine is based ...
Zināʾ ( زِنَاء) or zinā ( زِنًى or زِنًا) is an Islamic legal term referring to unlawful sexual intercourse. [ 1][ 2] According to traditional jurisprudence, zina can include adultery, [ 3][ 4][ 5] fornication, [ 3][ 4][ 5] prostitution, [ 6] rape, [ 2] sodomy, [ 3][ 7] incest, [ 8][ 9] and bestiality. [ 3][ 10] Zina must be ...
The exception proves the rule is a phrase that arises from ignorance, though common to good writers. The original word was preuves, which did not mean proves but tests. [ 4] In this sense, the phrase does not mean that an exception demonstrates a rule to be true or to exist, but that it tests the rule, thereby proving its value.
Mathematical fallacy. 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 ...
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. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...