# Is there a name for subtracting a set of values from their max?

I hope this question is appropriate here - if it isn't let me know and I will remove it.

I am wondering if there is a verb for the following operation: given a set of non-negative numbers, I take their max and then subtract the numbers from the max. This essentially "flips" the order of the numbers and makes the (previous) max zero.

I would like to say something like "I flipped the numbers" or describe it very shortly.

The context is that I am describing various transformations applied to a data set, e.g. "I standardized the data so that $\mu = 5$ and $\sigma = 1$ then log-transformed the data, and finally flipped it."

Any ideas?

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So.. you have a set $S=\{a,\dots\}$ with $a=\max S$ and you construct $T=\{a-s:s\in S\}$. Is this what you mean? – Karl Kronenfeld Jul 31 '13 at 1:41
This isn't really flipping. The smallest element will still be the smallest element, and the largest element will still be the largest element (that is, it will be 0, while the rest will all be negative numbers). – Ataraxia Jul 31 '13 at 1:46
@Ataraxia: He's taking the set $\{max - a : a \in S\}$, not $\{a - max : a \in S\}$. Bitwise: No, there's no name for this. – Eric Tressler Jul 31 '13 at 1:48
@user1 and Eric yes, that's it. – Bitwise Jul 31 '13 at 1:49
@EricTressler Oh ok, then that is flipping. Sorry for the mistake. – Ataraxia Jul 31 '13 at 1:49

Let $(x_1,x_2,\ldots, x_n)$ be the given list of numbers, and let $s:=\max_{1\leq k\leq n} x_k$. Then I'd call $d_k:=s-x_k\geq0$ the defect of $x_k$, so that $(d_1,\ldots,d_n)$ would be the list of defects of the given data.