BELIEVE   ME   NOT!    - -     A   SKEPTICs   GUIDE  

. . . error).^5.1

More on this later . . . .

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. . . thing;^5.2

"Uncertainty" is somewhere in between.

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. . . $\delta x$?^5.3

Notational convention: we use $\Delta x$ to denote "a change in x, not necessarily tiny" whereas $\delta x$ usually means "a little bitty change in x, but definitely finite!" and dx means "a change in x that is so teensy that it can be neglected relative to anything else but another really teensy thing." That last one (dx) is called a "differential" - Mathematicians don't like it much but Physicists use it all the time.

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. . . by:^5.4

The symbol ${\displaystyle \sum_{i=1}^N}$ represents an operator called "summation" - it means that {the stuff to the right of the $\Sigma$}, which will always have a subscript _i in one or more places, is to be thought of as the " $i^{\rm th}$ term" and all such terms with i values running from 1 to N are to be added together to form the desired result. So, for instance, ${\displaystyle \sum_{i=1}^N} \; x_i$ means $\{x_1 + x_2 + x_3 + \dots\ + x_{N-1} + x_N\}$, or (to be more specific) if N=3, just $\{x_1 + x_2 + x_3\}$. This may seem a little arcane, but it is actually a very handy compact notation for the rather common summation operation.

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