theory like coordinate geometry

sadhu

is one -one correspondence must for a theory like coordinate geometry , polar coordinate ,vector analysis etc
to work , i.e theories which work by representing a quantity by a different set of quantities
behaving alike

Hurkyl

It's hard to tell exactly what you're asking... but I think I can answer.

It is fairly common to allow many different notations for the same object; you just have to include rules for identifying when two notations denote the same object.

e.g. 1/2 and 2/4 are two different notations for the same rational number, and 0° and 360° are two different notations for the same angle. (0° and 360° are different angular displacements, of course)

sadhu

what i meant was like in vector we represent a vector by a straight directed line and then use its property to find the property of the represented vector .

this is because they belong to same class of entities i.e vectors

similiarly ordered triplets and points are two quantities which represent each other in space