Respuesta :
Answer:
Step-by-step explanation:
Given that there are 101 people of different heights standing in a line
Consider the number 101
It is of the form
[tex]n^2+1\\= 10^2+1[/tex]
By application of Ramsey theory, any sequence consisting of [tex]n^2+1[/tex] distinct numbers contains a subsequence of length n+1 that is either decreasing or increasing.
Here we have 101 with n =10
Since 101 people are having different heights, we must have 10+1 heights i.e. heights of 11 people either increasing or decreasing.
Since 101 people should have different heights, so it should have 10+1 heights.
Impact on heights:
Since
There are 101 people of different heights standing in a line
So here we Consider the number 101
It is of the form like
[tex]= n^2 + 1\\\\= 10^2 + 1[/tex]
Now here we apply Ramsey theory, any sequence that comprise of distinct numbers should contain a subsequence of length n+1 that is either decreasing or increasing.
Learn more about height here: https://brainly.com/question/24313591
