In boundary-value analysis, why test min+1 along with min?

In boundary analysis testing, some authors suggest testing MIN-1, MIN, MIN+1 (and the same for MAX).

Also for 1-100 range (if A>=1 && A<=100), test cases would be: 0,1,2 and 99,100,101.

I do not see the point - if 100 works, then 99 must work too (in my opinion but this is why I ask).