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So what you are saying is that if you don't know what can go wrong then it's "obviously true."

Let's try some other things.

* If you draw a distorted circle in the plane then it's obviously true that it has an inside and an outside.

* The inside is obviously contractable to a point, and the outside is obviously contractable to a plane with a hole in it.

* In three dimensions if you have a distorted sphere then it obviously divides space into an inside and an outside.

* The inside is obviously contractable to a point, and the outside is obviously contractable to 3D space with a hole in it.

All obvious, right?

Now, pick the statement (or statements) from the above that are in fact false.




>>So what you are saying is that if you don't know what can go wrong then it's "obviously true."

I never claimed that. I only claimed that FTA is obvious and that pointing out that something similar to FTA on some complex objects (a + sqrt(-5) things) doesn't work isn't a correct way to argue the FTA itself isn't obvious.

>>If you draw a distorted circle in the plane then it's obviously true that it has an inside and an outside.

Yes (as long as definition of "distorted" doesn't contain any surprises, I am assuming you mean not exactly a circle but something like it).

>>The inside is obviously contractable to a point, and the outside is obviously contractable to a plane with a hole in it.

Those things already aren't obvious. Go ask someone a bright kid in high school what "contractable to a plane" is. It's not obvious in any way to non-mathematician.

I am claiming FTA is obvious for a bright person who understand multiplication (or for a caveman who can do multiplication by putting rectangles together, then making rectangles from those rectangles etc.)

>>In three dimensions if you have a distorted sphere then it obviously divides space into an inside and an outside.

Yes, obvious.

>>The inside is obviously contractable to a point, and the outside is obviously contractable to 3D space with a hole in it

Again, those things are very far from obvious. What "contractable to 3D space with a hole" means is very far away from "obvious" by any reasonable definition of the word.


Please eventually provide the answer, because I'm curious!


The correct spelling "contractible" yields useful Google results, namely that spheres in 3 dimensions (point 4) are not contractible to a single point.

Edit: ... and maybe circles (point 2) too? Not a mathematician.


> The correct spelling "contractible" yields useful Google results, namely that spheres in 3 dimensions (point 4) are not contractible to a single point.

The claim is about the interior, not the sphere itself (which certainly is not contractible, as you say).


You have email.




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