Set.
The notion of a set is the most fundamental in Mathematics. Careless use of sets leads to contradictions the most famous of which was discovered by Bertrand Russell. Without going into details, sets are collections of elements that share some property P - the characteristic property of a set. The following notation is quite common: {x: P(x)} is read "the set of all x that have the property P". In view of the possibility of paradoxes, it must be remarked that not every possible property P defines a set.

Similarity.
Two triangles are similar if they have equal angles in which case their corresponding sides, say, a1, b1, c1 and a2, b2, c2, are proportional with a coefficient r: a1/a2 = b1/b2 = c1/c2 = r. Since side length could be looked at as the distances between the vertices, going from one triangle to another modifies these distances by a factor of r. Distances between other corresponding points in the triangles also change by the factor of r. This can be generalized. A similarity is such a transformation of the plane under which distance between any pair of points changes by the same factor. Similarity transformations play a central role in the Fractal Geometry and even more so in the theory of Iteration Function Systems (IFS). Consecutive Peano curves each consist of four images of itself each half the size of the whole. Similarity transformations are easily defined in spaces of higher dimensions.

Slope.
For a straight line in the plane, the slope is the tangent of the angle it forms with the positive X axis. For a curve (e.g., a graph of a function), the slope is, by definition, the slope of the tangent line. Therefore, if the slope is constant a line is straight.

Space.
There are too many different spaces in Mathematics to enumerate all. Generally, space is a set of points with additional features.

Stability.
Solution to a problem is stable if a small modification in the conditions of the problem does not change the solution too much. How much is much depends of course on the problem.

Subgroup.
A subset H of a group G is a subgroup (of G) provided it's a group with respect to the group operation of G.

Tree.

Trees, as special graphs, consist of nodes and edges and are best defined recursively. For every tree one node is singled out and is called the root. One node constitutes a tree and, naturally, is that tree's root. A collection of more than one node is a tree if by removing the root the remaining nodes fall into disjoint trees. Nodes connected to a tree root are called siblings.

A shorter way is to define the tree as a connected graph with no circuits. The absence of circuits means that there is always exactly one way to get from one vertex of the tree to any other.

As a basic data structure, tree is designed to easily store information about graph trees. In its commonest form a tree structure has pointers to the next sibling and the first child.

Unit price
The price of a single item or the price per kilogram or gram.

Unlike terms
Terms with different variables or the same variables raised to differentexponents .
e.g. 4x2 and 2x3.