/sci/ - Science & Math

>>15411143
>What country are you from
India.
I also have an entrance exam (in 2 weeks). Here is a question from it:

Let [math] a_1 < a_2 < \dots < a_m [/math] and [math] b_1 < b_2 < \dots < b_n [/math] be real numbers such that:
[eqn] \sum_1^m | a_i - x | = \sum_1^n | b_i - x | \qquad \text{for all } x \in \mathbb R [/eqn]
Show that [math] m = n [/math] and [math] a_i = b_i [/math] for all [math] i \in \{ 1,2, \dots , n \} [/math]
- Pdf anon