- #1
suyver
- 248
- 0
I just learned something really cool.
Choose 13 real numbers [tex]x_1,x_2,\ldots,x_{13}\in\mathbbb{R}[/tex] with [tex]x_i\neq x_j[/tex] if [tex]i\neq j[/tex]. For these 13 numbers there exist at least two numbers amongst them such that
[tex]0 \; < \; \frac{x_i-x_j}{1+x_ix_j} \; \leq \; 2-\sqrt{3}[/tex]
Isn't that cool?!
(I think I have a proof, but feel free to give it a go and post something ).
Choose 13 real numbers [tex]x_1,x_2,\ldots,x_{13}\in\mathbbb{R}[/tex] with [tex]x_i\neq x_j[/tex] if [tex]i\neq j[/tex]. For these 13 numbers there exist at least two numbers amongst them such that
[tex]0 \; < \; \frac{x_i-x_j}{1+x_ix_j} \; \leq \; 2-\sqrt{3}[/tex]
Isn't that cool?!
(I think I have a proof, but feel free to give it a go and post something ).