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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 from the origin, and the distance between one
location and another can be measured.
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