1. ## finding cardinality

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.

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

C={ $C_1 , C_2 , C_3 , .....$} where C is an element of real numbers
$\Rightarrow C \rightarrow$ to Real numbers $\Rightarrow [circles] \rightarrow$ [Real numbers x Real numbers]
$\Rightarrow rxr \mapsto$ 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

2. Hi

To answer the question, you can find what is necessary and sufficient to determine one circle (two parameters can do that job).
Then, let $A$ and $B$ be the sets of all possible parameters, $A\times B$ will be equipotent to the set of all circles in the plane, and you will be able to get its cardinality, which is the cardinality of $A\times B.$ I see some interesting words in what you wrote.

What are the parameters and then what are $A$ and $B$?