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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."

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.




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