This is enought to prove that, In 2D reference frame, everypoint is 2D.
1) We take P point .
We take A point from OX axis and add A,P as if AP | OX.
2) According to X-Coordinate, the location of the point is OA and according to Y-Coordinate, the location of the point is AP.
3) P point will be defined for those two dimensions.
4) Hence the location of the point in the S-reference frame is P(x,y).
5) Hence P point apparently 0D but according to the reference frame as that's not above of that,
Hence , that's 2D .(Proved)Suppose that S-reference is 1D .It has only X-Coodinate .We have to prove that ,In 1D reference frame,everything is 1D.This is enough to prove that ,in 1D reference frame , every objects point is 1D
1) We take P point from the OX axis.
2) The location of P point will be defined for the X-Coordinate.Apparently, that's OD.But according tp rrference frame , that is 1D.
3) Hence the location of the point is P(x)
:. Hence P point is 1D. That will be defined for the only X-coordinate and that's only 1 dimensional.So that's ultimately 1D.(Proved)Same cases for 0D .As the reference frame is 0D . Everything is 0 D.
To prove that , in 3D reference frame the center point of a sphere is 3D.
1) Suppose S-reference is 3D. There is a sphere which 3D but the center point is apparently 0D.We will prove that's 3D.
2) We mark as P. For the first ,We add P,obviously that will be directly beneath of
P point (With the surface of the frame)
We take a point B from the OX axis and
add AB as if that become AB | OX .
Hence , according to OX axis the location
of P point is OB ,according to OZ axis, the
location of P point is AB,according to OY
the location of P point is AP.
:. For the three dimensions,P point will be defined .Three dimensions are working for P point's existence. Hence P point is 3D . (Proved)
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