# Number of elements in a set.

i am just getting started with discrete mathematics and set theory and i came across this question which would seem like an elementary problem. I would appreciate any help on this :

Suppose $m$ and $n$ are positive integers with $m < n.$ How many elements does $[m,m+1,\dots,n]$ have?

I am not sure how to break down the logic here

• What is the question exactly? – WSL Apr 23 '15 at 23:07
• I think something must be missing here... – TravisJ Apr 23 '15 at 23:07
• i edited the question. Any help would be appreciated – sanster9292 Apr 23 '15 at 23:11

You could try it with a few small numbers and just count. Try $m=2,n=7$ and a few other pairs, for example. A more systematic approach: How many numbers are in $[1,2,\dots n]?$ How many are in $[1,2,\dots m-1]?$ How many are left?
$$\{1, 2, \ldots, m - 1, m, m + 1, \ldots n\} = \{1, 2, \ldots, m - 1\} \cup \{m, m + 1, \ldots n\}.$$
When $n=m+1$ the number of elements is $2=m+1-m+1$. In the general case the number of elements is $n-m+1$