Im curious, if there is a symbol for summation: $$\sum$$ then is there a symbol for difference? If not, if not how could I represent the difference of a sequence of numbers $(1-2-3-4-...)$?
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$\begingroup$$$a_1-a_2-\cdots - a_n= a_1-\sum_{k=2}^n a_k$$
$\endgroup$ $\begingroup$All you're doing is adding a bunch of negative numbers to 1. $1 - 2 = 1 + (-2)$, $1 - 2 - 3 = 1 + (-2) + (-3)$, $1 - 2 - 3 - 4 = 1 + (-2) + (-3) + (-4)$, etc. So you can just use the summation operator. Say you want to take this to $-10$: $$1 + \sum_{i = 2}^{10} -i.$$
By the way, take a look at A034856 in Sloane's OEIS.
In calculus, there's this thing called "finite difference," defined by Mathworld as "the discrete analog of the derivative." This concept does have some bearing on what you're talking about, but is not exactly what you're asking. I thought it was worth mentioning.
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