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Yes, all geometry planes are infinite and have lines going in every direction, except it doesn't look like that when you see a grid because they only need to include some information for a certain part of a line of the plane. All lines go forever in each direction (left and right), and a grid is made up of lines.

Q: In geometry can a plane contain an infinite number of lines?

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Yes, in Euclidean geometry, an infinite number of lines can meet at one point.

None. In ordinary geometry, a line contains an infinite number of points and, by definition, they are all collinear. In projective geometry, however, you can have three lines in the form of a triangle. Each line has only two points on it, so it cannot have 3 points collinear.

It is the parallel lines in Geometry!

In Euclidean planar geometry, not unless they're collinear, in which case they intersect an infinite number of times. In other types of geometry ... maybe.

No. In spherical elliptical geometry, for example, given the earth's North and South poles, there are an infinite number of lines of longitudes between them.

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infinite number of lines

Yes, in Euclidean geometry, an infinite number of lines can meet at one point.

None. In ordinary geometry, a line contains an infinite number of points and, by definition, they are all collinear. In projective geometry, however, you can have three lines in the form of a triangle. Each line has only two points on it, so it cannot have 3 points collinear.

It is the parallel lines in Geometry!

In Euclidean planar geometry, not unless they're collinear, in which case they intersect an infinite number of times. In other types of geometry ... maybe.

No. In spherical elliptical geometry, for example, given the earth's North and South poles, there are an infinite number of lines of longitudes between them.

infinite

A cylinder has an infinite number of lines of symmetry (because a circle has an infinite number of lines of symmetry).

Geometry teaches there are an infinite number of semi-circles for a sphere. Hence in the grid system that creates the longitude lines that form semi-circles, it becomes the same as what is taught in geometry = infinite number. If you limit yourself to using a llimited definition to units of whole degrees, then 360 semi-circles. However, I suspect that the answer you need is Infinite.

Yes the lines within the Cartesian plane are infinite

A sphere has an infinite number of lines of symmetry

In plane geometry a line is a two dimentional object between two points. If a line or a point is not on the line it, by definition, does not contain them. The answer therefor is infinite. Unless it is a closed line which has a slightly different definition but the answer is the same.