I'm stuck with part e of the following question:
$let R_i = \{ x \in \Bbb R | 1 \le x \le 1 + \frac1 i \} = [ 1, 1 + \frac1 i ]$ foreach positive integer $i$.
Now, for part e I thought it was simple enough but when I compared to the prof's answers mine was wrong, but I'm really unsure.
Part e: $\bigcap_{i=1}^nR_i=?$
My answer for this question is the following interval: $\bigcap_{i=1}^nR_i=[1, 1 + {1\over n}]$
But the prof had the following: $\bigcap_{i=1}^nR_i=\{1\}$
This doesn't make sense to me as as the smallest interval (in this case $[1, 1 + {1\over n}]$) would be a subset of all the sets from 1 to n (thereby being the intersection of all the sets from 1 to n).
If I'm mistaken, could someone break this down a bit for me? I really don't understand how the answer could be $\{1\}$