/sci/ - Science & Math

>>12428144
>>12428209
solution for the statement without abs value:
assume the condition is true for a function f on an interval [a, b], choose some n
then for each x in the interval, you can pick [math]l_x < x < r_x[/math] such that [math]\frac{f(p) - f(x)}{p - x} > n[/math] for all [math]p \in (l_x, r_x)\setminus \{ x \}[/math]
so this implies [math]\frac{f(p) - f(q)}{p - q} > n[/math] for all [math]p, q \in (l_x, r_x)\setminus \{ x \}[/math]
now by compactness choose a finite covering of [a, b] by the intervals [math](l_x, r_x)[/math] and fuck around to get [math]f(b) - f(a) \geq n(b-a)[/math]
but obviously that can't be true for all n, so there's a contradiction

>>11863323
>>11863332
that's a nice picture

>>11863408
i heard it's being superseded by uber geometry, though