Modulus
I thought since distinct is written, the first option is eliminated as b coule be equal to a or c
1
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“distinct” only applies to a and c, not b.
The condition |a − b| + |b − c| = |a − c| is the triangle equality case, which happens only when b lies between a and c (including endpoints). So mathematically, b ∈ [a, c] or [c, a].
Now since the question says a and c are distinct, it just ensures the interval is proper (not a single point). It does NOT restrict b from being equal to a or c.
So option 1 is still valid.
Oh okay
Thank you so much!