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The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

The identric mean is defined by I(a,b)=1/e((b^b)/(a^a))^(1/(b-a)) for a>0, b>0, and a!=b. The identric mean has been investigated intensively and many remarkable inequalities ...

A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed.

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the image of f, also called the range of D under f, is defined as the set of all values that ...

Three impossible ways to combine four bars.

An impossible figure that locally (but only locally!) looks like a torus.

A p-form alpha is indecomposable if it cannot be written as the wedge product of one-forms alpha=beta_1 ^ ... ^ beta_p. A p-form that can be written as such a product is ...

A continuum that is not decomposable is an indecomposable continuum.

An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. The understanding of infinitesimals was a major ...

In a category C, an initial object is an object I in Ob(C) such that for any other object X in Ob(C), there is one and only one morphism from I to X.