Delta is the change in a value.
Using the term "delta" on the one hand, how, on the other hand, would you refer to the base value from which the given delta is derived? Is there a more precise term than "base value", or "value"?
(It also occured to me that delta is congruent to "relative". Does this make the base value "absolute"?)
Here is my view of $\Delta$ (the following is a piece of abstract nonsense):
To any function $f:\>{\mathbb R}^n\to{\mathbb R}^m$ is naturally (i.e., without further input) attached a function $$\Delta f:\quad {\mathbb R}^n\times{\mathbb R}^n\to{\mathbb R}^m\times{\mathbb R}^m\ ,$$ defined by $$\Delta f(x,X):=\bigl(x,\ f(x+X)-f(x)\bigr)\ .$$ This $\Delta$-functor satisfies the chain rule: $$\Delta(g\circ f)=\Delta g\circ\Delta f$$ (check it, beginning with the right hand side!). The interesting part of $\Delta$ is of course its second component $$\Delta_2f(x,X)=f(x+X)-f(x)\ ,$$ by itself a function of two variables. It is customary to suppress the little ${}_2$ and the dependence on the first variable in the notation, and in this vein one simply writes $$\Delta f: \quad X\mapsto f(x+X)-f(x)\ .$$ The above applies in particular to the identity function $x\mapsto x$, also called a variable and being denoted by $x$, or $y$, as the case may be. This $x$ is then the base variable, or reference variable, whereas $\Delta x$ is something which is derived from this variable $x$. I'd strongly discourage speaking of "base value"; since a value is something fixed once and for all, and all information about how this value came about is disregarded. Even less appropriate is bringing in the word "absolute". Its hurting enough when people talk about an "absolute maximum" when in reality a global maximum is meant. The notion of "absolute" should be restricted to the absolute value of real or complex numbers and such.
