Tangents

I used to get really mindfucked by tangents.  How can a line intersect with a point on a circle to form a ninety degree angle with the line only touching one point?  A circle is made of an infinite number of points.  Points have no width or height.  How can a line hit only one exact point on the circle without brushing into an infinite number of points right next to it that make up its curve?

It's a set of points where the supremum is in the set.

What the hell is that?  A comicbook character?

>>1
The points all have a specific position in space, yeah? Think of it like the Pauli exclusion principle—only one point can exist at a certain coordinate in space (not necessarily true, of course, but for sake of example). If the tangent hit more than one point, you can reductio ad absurdum it—that point would not fit the definition of a circle, i.e., it would not lie in the locus of points equidistant from a single point in space.

Think of it like the Pauli exclusion principle,


lol wut

I think the problem here is that the OP is failing to acknowledge that both the line of the circle and the tangent line are not just thin, they have no width dimension. They aren't even infinitessimally thin, they have zero fucking thickness.

>>2
>>3
HAHA:)

gb2 real analysis

>>5
Remember, like, back in high school chemistry, when they were teaching you the quantum mechanical model of the atom? The Pauli exclusion principle states that no two electrons of the same four quantum numbers can occupy the same orbital. That's why an orbital can only hold two electrons, and they have to be of different spins.

RON PAUL /sci/,

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