Differentials

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Section 3.3 Differentials

We will usually write infinitesimal numbers in the form $dQ\text{.}$ Such symbols are called differentials.

Thus, $dx\cong0\text{,}$ and non-infinite hyperreal numbers always look like either $r$ or $r+dx\text{,}$ for some real number $r\text{.}$ You can therefore think of the (non-infinite) hyperreal numbers as consisting of the real numbers together with numbers that are “close” to them, in the formal sense that $r+dx\approx r\text{.}$

We will have more to say about differential notation later, and in particular the relationship between $dQ$ and $Q\text{.}$