$\newcommand{\vf}{\mathbf{\boldsymbol{\vec{#1}}}} \renewcommand{\Hat}{\mathbf{\boldsymbol{\hat{#1}}}} \let\VF=\vf \let\HAT=\Hat \newcommand{\Prime}{{}\kern0.5pt'} \newcommand{\PARTIAL}{{\partial^2#1\over\partial#2^2}} \newcommand{\Partial}{{\partial#1\over\partial#2}} \renewcommand{\SS}{\vf A} \newcommand{\dS}{dA} \newcommand{\dA}{dS} \newcommand{\MydA}{dA} \newcommand{\dV}{d\tau} \newcommand{\RR}{{\mathbb R}} \newcommand{\HR}{{}^*{\mathbb R}} \newcommand{\BB}{\vf B} \newcommand{\CC}{\vf C} \newcommand{\EE}{\vf E} \newcommand{\FF}{\vf F} \newcommand{\GG}{\vf G} \newcommand{\HH}{\vf H} \newcommand{\II}{\vf I} \newcommand{\JJ}{\vf J} \newcommand{\KK}{\vf K} \renewcommand{\aa}{\VF a} \newcommand{\bb}{\VF b} \newcommand{\ee}{\VF e} \newcommand{\gv}{\VF g} \newcommand{\iv}{\vf\imath} \newcommand{\rr}{\VF r} \newcommand{\rrp}{\rr\Prime} \newcommand{\uu}{\VF u} \newcommand{\vv}{\VF v} \newcommand{\ww}{\VF w} \newcommand{\grad}{\vec\nabla} \newcommand{\zero}{\kern-1pt\vec{\kern1pt\bf 0}} \newcommand{\Ihat}{\Hat I} \newcommand{\Jhat}{\Hat J} \newcommand{\ii}{\Hat\imath} \newcommand{\jj}{\Hat\jmath} \newcommand{\kk}{\Hat k} \newcommand{\nn}{\Hat n} \newcommand{\NN}{\Hat N} \newcommand{\TT}{\Hat T} \newcommand{\ihat}{\Hat\imath} \newcommand{\jhat}{\Hat\jmath} \newcommand{\khat}{\Hat k} \newcommand{\nhat}{\Hat n} \newcommand{\rhat}{\HAT r} \newcommand{\shat}{\HAT s} \newcommand{\xhat}{\Hat x} \newcommand{\yhat}{\Hat y} \newcommand{\zhat}{\Hat z} \newcommand{\that}{\Hat\theta} \newcommand{\phat}{\Hat\phi} \newcommand{\DD}{D_{\hbox{#1}}} \newcommand{\LargeMath}{\hbox{\large#1}} \newcommand{\INT}{\LargeMath{\int}} \newcommand{\OINT}{\LargeMath{\oint}} \newcommand{\LINT}{\mathop{\INT}\limits_C} \newcommand{\Int}{\int\limits} \newcommand{\dint}{\mathchoice{\int\!\!\!\int}{\int\!\!\int}{}{}} \newcommand{\tint}{\int\!\!\!\int\!\!\!\int} \newcommand{\DInt}{\int\!\!\!\!\int\limits_{#1~~}} \newcommand{\TInt}{\int\!\!\!\int\limits_{#1}\!\!\!\int} \newcommand{\Bint}{\TInt{B}} \newcommand{\Dint}{\DInt{D}} \newcommand{\Eint}{\TInt{E}} \newcommand{\Lint}{\int\limits_C} \newcommand{\Oint}{\oint\limits_C} \newcommand{\Rint}{\DInt{R}} \newcommand{\Sint}{\int\limits_S} \newcommand{\Item}{\smallskip\item{\bullet}} \newcommand{\LeftB}{\vector(-1,-2){25}} \newcommand{\RightB}{\vector(1,-2){25}} \newcommand{\DownB}{\vector(0,-1){60}} \newcommand{\DLeft}{\vector(-1,-1){60}} \newcommand{\DRight}{\vector(1,-1){60}} \newcommand{\Left}{\vector(-1,-1){50}} \newcommand{\Down}{\vector(0,-1){50}} \newcommand{\Right}{\vector(1,-1){50}} \newcommand{\ILeft}{\vector(1,1){50}} \newcommand{\IRight}{\vector(-1,1){50}} \newcommand{\Partials} {\displaystyle{\partial^2#1\over\partial#2\,\partial#3}} \newcommand{\Jacobian}{\frac{\partial(#1,#2)}{\partial(#3,#4)}} \newcommand{\JACOBIAN}{\frac{\partial(#1,#2,#3)}{\partial(#4,#5,#6)}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&}$
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 $Q\text{.}$