Figure 1: Graph of y = 2x - 3 in Euclidean 2-space. |
A mathematical space is a set of properties governing the interaction of objects contained in the space.
A common example of a space is Euclidean 2-space. An x-y graph exists in Euclidean 2-space. The word Euclidean means that objects have the properties associated with Euclidean geometry, most importantly the fifth postulate which controls the intersection of lines. The 2 in 2-space refers to the fact that this space has two dimensions: length and width.
The term n-space is used to define a space with n dimensions. For example, a 2-space is a space with 2 dimensions. A 3-space is a space with 3 dimensions.
Some spaces that are often used in mathematics are:
One attribute that a space can have is a metric space. In a metric space, location can be measured.
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