Prove me wrong

>A circle isn't a series
correct, it's a set of points

A circle of radius r are the set of points (x,y) where x^2+y^2=r^2

Calm down, circle idea is an axiom. Such as circle is an 2d shape with an infinite number of corners.

A circle is an infinite set of points. We may show that this is consistent with the fact that circles have non-zero circumference.

Pick a central point about which to draw your circle. Now, draw a vertical line (along 90 degrees) of length r. Draw a point at the end of this line. Next, draw an identical line and point rotated 120 degrees about your central point. Do the same one more time 120 degrees from this second line.

This gives you three points of a triangle. Sum the edge lengths, and this is your order-3 approximation.

Next, repeat this process from scratch using 4 lines in 90 degree increments (obtaining a square). Then 5 lines in 72-degree increments (obtaining a pentagon). Derive the closed form for the perimeter of an order-x approximation to the circumference of the circle, and then take the limit as x goes to infinity. You'll see that the circumference (this limit) is non-zero but that the circle itself is transcribed by an infinite number of points.

>A circle isn't a series of a infinite points. A point has no length so when you add them together you will still just have a 0 length point, not a circle.
>A circle isn't a series
Right
>of a infinite points
English please, this has no meaning.
If you mean "an infinite series of points" you are wrong. "Series" have a whole different meaning.
>A point has no length
Right
>so when you add them together
What do you add together? The points length? You just said they didn't have any... It's not that their length is 0, they just don't have a length. They don't even have a dimension in which to measure lengths.
>you will still just have a 0 length point.
You don't have a single point, but it doesn't even matter, as we saw they don't have a length.
>not a circle.
Well, what more can I say?

If you want to play on the edges of mathematics definitions, you have to be clear and precise.
Your sentence isn't wrong or right, it has no meaning.
Just as "What is the color of 'mindset'"
It doesn't have an answer.

Is dat sum Klein Frog?

By that rationale, the "real" line R is also not a line, but just a 0 lenght point?

Please remember that (∞ × 0) ≠ 0. It's am indeterminate form
>en.wikipedia.org/wiki/Indeterminate_form

R/Z gives you a nice circle