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jeremy22511
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If there is a bijection between R and R2, then why can't a point on a plane be represented by one real number instead of two?
jeremy22511 said:If there is a bijection between R and R2, then why can't a point on a plane be represented by one real number instead of two?
Points on a plane refer to the specific locations or coordinates on a two-dimensional surface. They are important because they allow us to represent and analyze geometric shapes and objects, and they are essential in fields such as mathematics, physics, and engineering.
Points on a plane can be represented using a coordinate system, such as the Cartesian coordinate system. In this system, a point is represented by two numbers (x, y) where x represents the horizontal position and y represents the vertical position of the point on the plane. Alternatively, points can also be represented using a single number, known as the polar coordinate system, where the number represents the distance from the origin and the angle from a reference line.
Representing points on a plane with 1 real number uses a different coordinate system (polar) compared to representing them with 2 real numbers (Cartesian). The polar coordinate system is useful when dealing with circular or spherical shapes, while the Cartesian coordinate system is more suitable for representing straight lines and rectangular shapes.
Yes, points on a plane can also be represented using complex numbers. This is known as the Argand diagram, where the real part of the complex number represents the horizontal position and the imaginary part represents the vertical position of the point on the plane.
Points on a plane have a wide range of real-world applications, such as in navigation systems, mapping and surveying, computer graphics, and even in predicting the trajectory of objects in physics and engineering. They are also used in everyday tasks, such as reading maps and following directions.