Fur Mat's Last Theorum

It occurred to me in a flash of brilliance today that, for dog quantities greater than 2, there is no number of grooming sessions that will remove sufficient fur to prevent either matting that requires trimming out with scissors or the gross distribution of fur particles across every point in a plane consisting of the concatenation of all vertical and horizontal surfaces in the house including dark-colored clothing.

I can prove it, too, and I'd scribble the proof in the margin here except that blogs don't seem to have margins.

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