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Suppose we have an interval $[x_{min}, x_{max}]$ (where $x_{min} \gt x_{max}$) and a quantity $x$ that is a member of this interval. Is there a name for the following quantity?

$\frac{x - x_{min}}{x_{max} - x_{min}}$

The best way I can describe this is as the ratio of $x$'s "distance" from the minimum to the "length" of the interval. When $x = x_{min}$, this is $0$, and it's $1$ when $x = x_{max}$.

jpmc26
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    When $x=x_{max}$, it's actually $-1$. –  Feb 14 '14 at 02:04
  • @SanathDevalapurkar Oh, pooh. Typos. Thanks. Fixing. – jpmc26 Feb 14 '14 at 02:06
  • You could call it a linear ramp from $0$ to $1$ over $[x_\min,x_\max]$. –  Feb 14 '14 at 03:47
  • @Rahul I've never heard of a linear ramp. Do you have a source that could flush out what it is? I Googled, and not much came up. – jpmc26 Feb 14 '14 at 06:31
  • If I don't get a clear answer, I might dub this the "relative interval position" (or r.i.p. XD) for lack of a better term. – jpmc26 Feb 14 '14 at 20:12

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Well, I'd call that a function, say $f$, with domain $[a,b]$, $$f(x)=\frac{x-a}{b-a}$$

It is exactly the same thing if you place $x_{min}$ for $a$ and $x_{max}$ for $b$. And yes, it describes the ratio of the distances you're saying.

frabala
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  • I appreciate the answer, but by "a name for the quantity", I mean something terse to help me communicate with colleagues. =) Calling it a "function" is pretty vague and won't communicate what quantity I'm talking about very clearly. Granted, I might have to explain a more detailed term to them, but once I do, it's easy to refer to it. At the moment, about all I have is "percentage thing" (since in my actual usage, I'm multiplying by 100). – jpmc26 Feb 14 '14 at 02:41
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    Ok, at least I make people laugh :D – frabala Feb 14 '14 at 02:44