What if there is $\downarrow$ or $\uparrow$ notation in the limit instead of $\rightarrow$?

Question

I saw a different notation in a limit in the book Elementary Differential Geometry by A. N. Pressley :

$\qquad$ If the Möbius band were orientable, there would be a well defined unit normal $\bf N$ defined at every point of $\cal S$ and varying smoothly over $\cal S$. At a point $\boldsymbol{\sigma}(0,\theta)$ on the median circle, we would have $${\bf N}=\lambda(\theta){\bf N_{\boldsymbol{\sigma}}},$$ where $\lambda:(0,2\pi)\to\bf R$ is smooth and $\lambda(\theta)=\pm1$ for all $\theta$. It follows that either $\lambda(\theta)=+1$ for all $\theta\in(0,2\pi)$, or $\lambda(\theta)=-1$ for all $\theta\in(0,2\pi)$. Replacing $\bf N$ by $-\bf N$ if necessary, we can assume that $\lambda=1$. At the point $\boldsymbol{\sigma}(0,0)=\boldsymbol{\sigma}(0,2\pi)$, we must have (since $\bf N$ is smooth) $${\bf N}=\lim_{\theta\downarrow0}{\bf N}_{\boldsymbol{\sigma}}=(-1,0,0)$$ and also $${\bf N}=\lim_{\theta\uparrow2\pi}{\bf N}_{\boldsymbol{\sigma}}=(1,0,0).$$ This contradiction shows that the Möbius band is not orientable.

what do both of $\downarrow$ and $\uparrow$ mean?

Answer 1

^{Answering this question so that it no longer remains unanswered.}

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Maybe limit "from above" and limit "from below" respectively? – AdLibitum