Generic propertyIn mathematics, properties that hold for "typical" examples are called generic properties. For instance, a generic property of a class of functions is one that is true of "almost all" of those functions, as in the statements, "A generic polynomial does not have a root at zero," or "A generic square matrix is invertible." As another example, a generic property of a space is a property that holds at "almost all" points of the space, as in the statement, "If f : M → N is a smooth function between smooth manifolds, then a generic point of N is not a critical value of f.
Modulo (mathematics)In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional factor. It was initially introduced into mathematics in the context of modular arithmetic by Carl Friedrich Gauss in 1801. Since then, the term has gained many meanings—some exact and some imprecise (such as equating "modulo" with "except for").
Language of mathematicsThe language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc) with concision, precision and unambiguity. The main features of the mathematical language are the following. Use of common words with a derived meaning, generally more specific and more precise. For example, "or" means "one, the other or both", while, in common language, "both" is sometimes included and sometimes not.
Pathological (mathematics)In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand, if a phenomenon does not run counter to intuition, it is sometimes called well-behaved. These terms are sometimes useful in mathematical research and teaching, but there is no strict mathematical definition of pathological or well-behaved. A classic example of a pathology is the Weierstrass function, a function that is continuous everywhere but differentiable nowhere.
