I am unable to come up with a correct proof for these questions. I have what I think could be part of it, but I seem to fill in the rest of the proof with wrong steps. help or an explanation would be helpful. thank you.

Find the cardinal number of the following sets. justify your answer.

1). the set C of all circles lying in the plane

C={$\displaystyle C_1 , C_2 , C_3 , ..... $} where C is an element of real numbers

$\displaystyle \Rightarrow C \rightarrow $ to Real numbers $\displaystyle \Rightarrow [circles] \rightarrow $ [Real numbers x Real numbers]

$\displaystyle \Rightarrow rxr \mapsto $ Real numbers x Real numbers, where r is the radius of a circle

i am completely lost and i don't think i'm doing this right. thanks for the help.

Scott