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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

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

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Here's another approach.

Notice that we can write

$$\{1, 2, \ldots, m - 1, m, m + 1, \ldots n\} = \{1, 2, \ldots, m - 1\} \cup \{m, m + 1, \ldots n\}.$$

In other words, the set you're interested in has a nice relationship to two sets whose cardinalities you already know!

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When $n=m+1$ the number of elements is $2=m+1-m+1$. In the general case the number of elements is $n-m+1$

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