Point
A point is a 0-dimensional mathematical object which can be specified in 
-dimensional space using an n-tuple
(
, 
, ..., 
) consisting
of 
coordinates. In dimensions greater than or equal
to two, points are sometimes considered synonymous with vectors
and so points in n-dimensional space are sometimes
called n-vectors. Although the notion of a point
is intuitively rather clear, the mathematical machinery used to deal with points
and point-like objects can be surprisingly slippery. This difficulty was encountered
by none other than Euclid himself who, in his Elements,
gave the vague definition of a point as "that which has no part."
The basic geometric structures of higher dimensional geometry--the line, plane, space, and hyperspace--are all built up of infinite numbers of points arranged in particular ways.
These facts lead to the mathematical pun, "without geometry, life is pointless."
The decimal point in a decimal expansion is voiced as "point" in the United States, e.g., 3.1415 is voiced "three point one four one five," whereas a comma is used for this purpose in continental Europe.
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