Prove me wrong

>>8676127
You're right. It's not a series of points. It's a series very of infinitely small lines connecting infinitely small points infinitesimally close to one another

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>>8676129
>infinitely small lines
So zero length lines then, same thing as a point
>infinitesimally close together
So they're touching, but they can't touch because there's nothing to touch, points are 0x0x0

What you said doesn't even make sense but it still doesn't make a circle

so whats a circle then

>A circle isn't a series of a infinite points.
It's not. That's the Decartian model.

A point has no length so when you add them together you will still just have a 0 length point, not a circle.
Can you mathematical express what you mean by "adding" them together? For your line of thought, wouldn't even matter if you speak of a circle or a line or a cube or whatever.

You want there to be an injection [math] {\mathbb S} \to [0,end) [/math] first,
where S is your set of circle points and and [math] end\in {\mathbb R}_{>0}[/math] a real number. Then you can put a metric
[math] d : {\mathbb S} \times {\mathbb S} \to {\mathbb R}_{>0} [/math]
on the circle and this defines you notion of distance.

>>8676135
0*inf =/= 0

>>8676140
That round thingy where every point on the edge is equidistant to the shape's center.

>>8676140
A polygon where every edge point is equal distance from the center. Circles don't exist. Everything is a polygon.

>>8676149

actually it does

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>>8676140
Well it's basically just a hypothetical mathematical object that doesn't really exist like pi

Are you familiar with the concept of limit?

>>8676127
Of course it isn't a series of points, it's a set of points.

>>8676165
>>8676165
Whatever that's what I meant

>>8676160
actually it doesn't

>>8676172
The first zero isn't a zero then, it's an infinitesimal.

>>8676148
Points don't require length to construct well defined continuity in R.

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>>8676127
What is the lenght of this circle here then?

How fucking braindead do you have to be to entertain these kinds of discussions on a daily basis?

>>8676127
>what is a set
>what is a locus
>what is a measure

>>8676127
>length of line = sum of lengths of points
Gtfo you brainlet frogposter

>>8676127
>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.

>>8676127
>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.

>>8676127
Is dat sum Klein Frog?

>>8676127
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
>https://en.wikipedia.org/wiki/Indeterminate_form

R/Z gives you a nice circle