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There is no such thing as a two-dimensional space. By virtue of being a space, you are talking three dimensions. It sounds like what you're really asking is: What is a two-dimensional AREA bounded by an infinite set of points (or infinite number of sides - same thing)? Typically, that would be a circle...however you didn't specify the points all had to be equidistant from its center so it could be any irregular shape containing at least one curve (any curved portion would automatically have to contain infinite points). The best way to ask the question so that the only answer would be 'a circle' is: What is a two-dimensional area formed by an infinite set of points, all of which are equidistant from its center?

Q: What is a two dimensional space formed by an infinite set of points?

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infinite width, contains a plane and is three dimensional

In 2-dimensional space, a circle. In 3-dimensional space, a sphere.

An infinite number, since points take up no space.

3-d space.

There are only three coordinates. This indicates three points in 1-dimensional space (in which case there is no slope) or one point in 3-dimensional space (in which case there is no specific line).

Related questions

A space can be two-dimensional and infinite if it does not have defined bounds. Mathematically, this usually means no restrictions on the domain or co-domain of the two-dimensional space.

No, the two planes intersect at a line, which is an infinite number of points.

A mile is a set distance of space between two points. Because of the one dimensional nature of such measurements, it can be said that there are an infinite number of miles within Uruguay. This is because one dimensional objects don't take up any space in a two- or three dimensional world, since lines are infinitesimally thin, and points are infinitesimally small. By not taking airspace into account, we can gladly say that Uruguay does take up a measurable amount of two dimensional space. At the same time however, it still takes up an infinite amount of miles because a mile is a one dimensional measurement of space.

infinite width, contains a plane and is three dimensional

A VR world is a three-dimensional (3D) environment that contains infinite space and depth.

Space

Three dimensional space.

In 2-dimensional space, a circle. In 3-dimensional space, a sphere.

They could need three dimensional space. Although points are 1-dimensional objects, it is easy to have four points that need 3-d space: for example the vertices of a tetrahedron (triangular pyramid). Similarly, skew line will need 3-d space.

Space is a boundless, three dimensional set of all points. Collinear is a set of points that are all on the same line and is 3 or more points.

An infinite number, since points take up no space.

An infinite number, since points take up no space.