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#### paulmdrdo

##### Active member

- May 13, 2013

- 386

"there's a one to one correspondence between the length of all arcs in the Unit Circle and the set of real numbers."

my understanding to this is that there's a corresponding real number to the length of all arcs of the unit circle. like in the real number line.

but as i read further the books says "that there's a 1-1 correspondence between the set of real numbers and all angles $\theta$ in standard position."

my whole understanding to this is when we have a unit circle all lengths of arcs in the unit circle corresponds to a unique real number and all angles $\theta$ in the unit circle also correspond to a unique real number. it seems that the length of all arcs is also the measure of the angle $\theta$ subtended by an arc on the unit circle.

what will happen if have a circle different from the unit circle? will this statement still hold for any other circles?

please correct my wrong notion if there's any.