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A circle of zero radius is indiscernible from a circle of infinite radius.

>>11709438Okay now what?

>>11709438your sentence makes a distinction between the two by identifying they have different radii

>>11709447It's just an interesting reflection on how reality itself is a harmony of opposites. For example, the universe has net 0 energy, making it not much different from the lack of a universe.>>11709450Of course they're different. They're just indiscernible. See text above.

>>11709438a point is indiscernible from a straight line ?

>>11709470How so?

>>11709438you literally just discerned between them.>b-but they would look the same if instantiatedthey do not have looks. they are abstracts.

>>11709438a circle of radius r can be defined as the set {(x,y) : x^2+y^2=r^2}. a circle of radius 0 is the set {(0,0)} while a circle of radius infinity is the empty set. seems like two discernible sets to me(btw you're not using the word discernible in the rigorous mathematical sense)

>>11709472I'm asking OP. but he better say yes, because it's equivalent to his statement.

>>11709507>circle of radius infinity is the empty setnot always, only when the center is a honest point. if the center is an ideal point, the circle is a straight line.

>>11709438Bullcrap! There's a difference between a tiny circle and a bigass circle.

>>11709455>what is dialectical materialismIt gets more interesting when you consider the logical stipulations of the universe being the harmony of opposites. For all the shit Marx gets, most people outside academia haven't heard of dialectical materialism and it is extremely interesting.If this interests you anon I'd recommend you read into it, particularly Dialectics of Nature by Engels.

>>11709438>indiscernibleToo vague. What do you mean?

>>11709438A what is indiscernible from a what?You just said the exact same thing twice and they are blending into the void I cant even discern them from the rest of the gobbledygook buzzing through the ideosphere let alone from each other.

>>11709527this is a valid way of interpreting the question. I kinda forgot about the connection between lines and circles using Mobius transforms on Riemannian sphere

Circles have finite and positive radius. Otherwise they are not circles.

>>11709438>A thing which contains every conceivable point in its plane is equivalent to a thing which contains exactly one pointYa done goofed, good bait though.

>>11710281Correct answer. This board is full of brainlets who think they're smart.

>>11709438No you are wrong.

[eqn]\text{let }r = 0\\C = 2\pi r\\C = 2\pi(0)\\C = 0\\\\\text{let }r = \infty\\C = 2\pi r\\C = 2\pi(\infty)\\C = \infty[/eqn]They seem pretty different to me

>>11710281>>11710457to be fair, it is useful to consider straight lines in the complex plane as circles with infinite radius and centers at infinity. this way, you get closure under Mobius transforms on the rienman sphere

>>11709438And how do you construct a circle of a zero radius?

>>11709455>making it not much different from the lack of a universe

in so far as they are both circles, their quality is identical, only their quantities differ. welcome, op, to the world of forms

>>11709438A circle of infinite radius is a straight line. A circle of zero radius is a point.

>>11710843>A circle of infinite radius is a straight linewhat? explain

>>11712959Not that dude. The circle of infinite radius looks like a straight line to an observor that's standing right on the curve since the radius of curvature is so large that the circular curvature disappeared. god damn my brain does not work at 3am. IN BIG CIRCLE, YOU DONT FEEL CURVATURE SO ITS STRAIGHT. THINK EARTH, EARTH IS FLAT BUTTTTTTTTT ITS ROUNDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

>>11712982BASADO

>>11709438Not really since a circle of zero radius isn't a circle.

>>11712959consider the family of circles passing through the origin [math](0,0)[/math] and with their center on the x-axis:[eqn](x-r)^2+y^2=r^2[/eqn]expand and divide by r to obtain[eqn]\tfrac{x^2}{r} - 2x + \tfrac{y^2}{r} = 0[/eqn] now send [math]r \to \infty[/math], you get a straight line.

>>11709438>A circle of zero radius is indiscernible from a circle of infinite radius.Because they dont exist?

>>11712959>>11713025https://www.desmos.com/calculator/hymvmuh5l3

>>11712982>The circle of infinite radius looks like a straight line to an observor that's standing right on the curveThat's impossible if you really think about it

>>11709438Arrival?

>>11709438OP, if you're still there, was this a T-duality joke?

>>11709513Not OP but yes, turn the line on a third axis and it will become a point (as it comes toward you).