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On an oriented n-dimensional Riemannian manifold, the Hodge star is a linear function which converts alternating differential k-forms to alternating (n-k)-forms. If w is an ...

A formal theory is said to be incomplete if it contains fewer theorems than would be possible while still retaining consistency.

The use of the principle of mathematical induction in a proof. Induction used in mathematics is often called mathematical induction.

Two curves phi and psi satisfying phi+psi=0 are said to be linearly dependent. Similarly, n curves phi_i, i=1, ..., n are said to be linearly dependent if sum_(i=1)^nphi_i=0.

Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

∡A_2MA_3=∡A_2A_1A_3+∡P_2P_1P_3, where ∡ is a directed angle.

Monster-barring is a term coined by Lakatos (1976) to refer to the refining of a hypothesis to rule out nasty counterexamples (Bailey et al. 2007, p. 11).

A condition which must hold for a result to be true, but which does not guarantee it to be true. If a condition is both necessary and sufficient, then the result is said to ...

The branch of formal logic, also called functional calculus, that deals with representing the logical connections between statements as well as the statements themselves.

A primality test is a test to determine whether or not a given number is prime, as opposed to actually decomposing the number into its constituent prime factors (which is ...