There are many inequivalent ways of doing this, in general.

Actually to be a little bit more precise, there are 406 inequivalent primitive operations on at most 50 points.

(both sides have dimension 2 and the representations on the right are inequivalent).

A single knot or link can have many different inequivalent Seifert surfaces.

There are several inequivalent definitions of dimension in mathematics.

The number 6 has two inequivalent factorizations within this ring:

The term α-Mahlo is ambiguous and different authors give inequivalent definitions.

These two inequivalent classes yield spinor transformations of opposite sign.

Continuous Gâteaux differentiability may be defined in two inequivalent ways.

These predetermined roles can lead to inequivalent advantages to people classified in certain categories over others.

The dual representation, which is inequivalent, is also 27-dimensional.

According to Haag, charge is a label for inequivalent representations of the algebra.

The 88 inequivalent rules are as follows, evolved from random initial conditions:

The second factor sums over different values of f that are inequivalent gauge fixings.

There are several inequivalent compactifications of Teichmüller spaces that have been studied.

It also lists the number of inequivalent (i.e. nonhomeomorphic) topologies.

Note, this is not a sequence of inequivalent cusps of the corresponding group.

Mixtures of products may result from attack at inequivalent ortho or para positions.

And you cannot just say "because 'good' and 'N' are analytically inequivalent".

Lebesgue measure and Dirac measure on the real line are inequivalent.

As recently as 1891, it was finally proved that there are only 17 inequivalent symmetry patterns in the plane.

Let be a complete set of inequivalent irreducible representations of .

Various inequivalent definitions of Kleene algebras and related structures have been given in the literature.

Every compact topological 2-manifold (possibly with boundary) can be turned into a Klein surface, often in many different inequivalent ways.

However, it is possible for two inequivalent knots to have isomorphic knot groups (see below for an example).