On quantifying the trouble of cats
An observation based on having n=1, 2, 3 cats.
Let 𝒯(n) be the amount of trouble caused by n cats.
One cat is trouble: 𝒯(1) > 0
Two cats are less trouble than twice the trouble of one cat: 𝒯(2)/2 < 𝒯(1)
Three cats are about as much trouble per cat as two cats: 𝒯(3)/3 ≃ 𝒯(2)/2
On quantifying the trouble of cats
Plotting trouble per cat as a function of number of cats produces this graph:
On quantifying the trouble of cats
@futzle It wouldn't surprise me at all. I love e and it seems a much more catlike number than pi.
On quantifying the trouble of cats
@futzle I have some questions about your curve of best fit extending below 1 on the X axis
On quantifying the trouble of cats
@futzle perhaps its asymptotic? lim(cat)→+0 = ∞
On quantifying the trouble of cats
@s0 It’s 0/0 so indeterminate. Application of L’Hôpital’s rule maybe.
On quantifying the trouble of cats
This suggests that there is a minimum amount of trouble per cat between 2 and 3 cats. In this proof, I will show that the minimum trouble per cat is precisely ℯ cats.