Someone made an argument that circles of different radii can't

All circles have the same cardinality

>>8761645
as long as there is a bijective function for mapping points between two circles, they have exactly the same (infinite) amount of points. (and yes, there are bijective functions)

>>8761645
>then there will be gaps between rays
This just seems false though.

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I'm not asking if the argument is right, I'm asking who made it. It is famous, come on help me out here.

>>8761699
It is retarded

I'm googling a bit and it seems cantor is the one who resolved the problem, not posed it
>http://blog.wolframalpha.com/2010/09/10/transfinite-cardinal-arithmetic-with-wolframalpha/
Some sites mention galileo as the originator of the problem although they don't use the ray argument.

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>>8761724
thankee. Cantor's argument seems, um... lacking.

So if I live Georgia, and infinity lives in California, is it far removed enough to resolve the paradox?

>>8761739
Yea it's a weird sentence, I noticed it too, but it's probably more the bloggers fault than Cantors. Cantors idea afaict is that if there is a one-on-one correspondence between two sets, they are the same size (cardinality).

>Mathematics knows no races
Yeah. That's why functions and associative math should be banned. Because it incites racism.
Anyone who has a part of the brain which has
associative cognitive abilities should be locked up and have a part of their brain removed and their intelligence castrated to acceptable and thought police approved levels.

>>8761756
>>>/pol/

>>8761739
That's not his argument, that's the result of his argument.

>>8761768
>>>/mlp/

>>8761662
even a circle with radius 0?

>>8761756

Triggered!

>>8761789
good question

>>8761789
There is no circle with radius 0, just like there isn't triangle with 3 points on the same line, or any geometric object with all points in same position.

>>8761890
>just like there isn't triangle with 3 points on the same line
There is. You just don't see it because it fell on the side like your IQ.

>>8761756
Sorry, but I don't listen to /pol/tards. My studies show they are associated with cognitive deficiency.

>>8761890
>The circle of radius r and center C is the set of points that are at a distance r from the point C.

With this definition, a circle of radius 0 does exist and is a singleton.