# The H value would be unique

• According to the definition of h, "if h of his/her N papers have at least h citations each, and the other N − h papers have no more than h citations each." Looks like the h value is unique. The "Note" part looks unnecessary.

Proof: say there exist two h-indices, h1 < h2 (1), which means that, there are h2 numbers have value at least h2 (2) and N-h2 values have value at most h2 (3); there are h1 numbers have value at least h1 (4) and N-h1 values have value at most h1(5).

We have (1)(2)(3), (1) and (2) implies (4), but we can see (5) is not possible. Because we have N-h1 > N-h2, there exists at least one paper not in the set of N-h2 but in the set of N-h1, this paper should have value <= h1 (according to 5) and have value >= h2 (according to 2), this contradicts to (1).

The uniqueness follows.

• Hi, just wanted to ask if the question is worded correctly, A scientist has index h if "atleast" h of his/her N papers instead of ----"A scientist has index h if h of his/her N papers"

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