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I recently came across this free website, and I've been using it to present ideas and explain things.

I recently asked a question which got a great answer by user Mateo. Using the website, I then condensed his answer into this picture:

enter image description here

I am considering posting this, with further pictures explaining why each arrow equivalence is true.

Would such answers be on-topic, even though image posts are generally frowned-upon here? Thanks.

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    $\begingroup$ If the answer is just the picture, as your example above, then anyone who has trouble with images (e.g. has some degree of blindness, though we're not limited to just that case) cannot benefit from your answer. If you want to deliberately exclude some of your potential audience that's your choice, but if not then you might want to think about how you'd be more inclusive. $\endgroup$
    – postmortes
    Jul 27, 2022 at 8:44
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    $\begingroup$ The image is beautiful. Do your best to reproduce it, though. Don't remove it. It looks really nice. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Jul 27, 2022 at 8:47
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    $\begingroup$ As postmortes says, this is deliberately exclusive, but this is not acceptable on Stack Exchange. Please don't make life more difficult just to show off a fancy toy. $\endgroup$
    – Nij
    Jul 27, 2022 at 11:27
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    $\begingroup$ No problem to showcase the image, as long as the crucial information within it is concurrently duplicated as actual text/mathjax. In other words, the post ought to be self-contained (and coherent) without that optional image. $\endgroup$
    – ryang
    Jul 27, 2022 at 11:50
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    $\begingroup$ Since the intended question was understood and answered here, I thought I'd take a moment to say it has nothing to do with being "on-topic." I can't imagine how an answer would be off-topic unless it did not attempt to address the question asked. What you're really asking is if the picture alone is considered good enough format to constitute an answer. $\endgroup$
    – rschwieb
    Jul 27, 2022 at 13:40
  • $\begingroup$ Isn't all useful technology start as fancy new toys in the beginning? $\endgroup$
    – Reine Abstraktion
    Jul 27, 2022 at 16:38
  • $\begingroup$ @Beautifullyirrational You could also manufacture the world's smallest encoding of the Oxford English dictionary in DNA using CRISPR, if one was that willing to sacrifice accessibility for toys. All i mean to say is that nifty tools make interesting additions but shouldn't be assumed to supplant the more obvious standard ones. $\endgroup$
    – rschwieb
    Jul 27, 2022 at 17:59
  • $\begingroup$ Okay I understand @rschwieb $\endgroup$
    – Reine Abstraktion
    Jul 27, 2022 at 18:32
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    $\begingroup$ It is great to use pictures as visual aids as part of a larger written answer. Picture only answers are not on-topic without further elaboration. For diagrams like this, TeX / MathJax is preferred, because the source text contributes to searchability and helps with rendering on different platforms. $\endgroup$
    – Alexander Gruber Mod
    Jul 29, 2022 at 2:53

1 Answer 1

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I disagree with including this particular picture. Your picture is a picture of text. Moreover, the flow of logic is linear, unlike other possible uses of diagrams of text. IMO it is enough to write

  1. Premise: we are in a compact subset
  2. In compact subsets, every sequence must have an accumulation point
  3. Every sequence has an accumulation point
  4. Bolzano-Weierstrass: Every sequence has a convergent subsequence

and then explain separately that there are the relations $2\rightarrow 3 \leftrightarrow 4.$ Or perhaps,

Premise: we are in a compact subset

In compact subsets, every sequence must have an accumulation point
$\rightarrow$Every sequence has an accumulation point
$\leftrightarrow$Bolzano-Weierstrass: Every sequence has a convergent subsequence

Premise: we are in a compact subset

In compact subsets, every sequence must have an accumulation point<br/>
  $\rightarrow$Every sequence has an accumulation point<br/>
  $\leftrightarrow$Bolzano-Weierstrass: Every sequence has a convergent subsequence

If you must use this diagram, it is not so hard to reproduce it in MathJax (because it is rather simple), which I find preferable to the picture, but it doesn't feel worth the effort in this particular case: $\newcommand{\mybox}[1]{\fbox{$\substack{#1}$}} \newcommand{\dtext}[1]{\displaystyle\text{#1}} \newcommand{\textone}{\dtext{Premise: we are in}\\\dtext{ a compact subset}} \newcommand{\texttwo}{\dtext{In compact subsets, every}\\\dtext{sequence must have an}\\\dtext{accumulation point}} \newcommand{\textthree}{\dtext{Every sequence has an}\\\dtext{accumulation point}} \newcommand{\textfour}{\dtext{Bolzano-Weierstrass:}\\\dtext{Every sequence has a}\\\dtext{convergent subsequence}} $ $$\fbox{$\begin{align} &\mybox{\textone} \\ & \begin{array}{ccccc} \mybox{\texttwo}&\rightarrow&\mybox{\textthree} \\&& \updownarrow \\ && \mybox{\textfour} \end{array} \end{align}$}$$

$\newcommand{\mybox}[1]{\fbox{$\substack{#1}$}}
\newcommand{\dtext}[1]{\displaystyle\text{#1}}
\newcommand{\textone}{\dtext{Premise: we are in}\\\dtext{ a compact subset}}
\newcommand{\texttwo}{\dtext{In compact subsets, every}\\\dtext{sequence must have an}\\\dtext{accumulation point}}
\newcommand{\textthree}{\dtext{Every sequence has an}\\\dtext{accumulation point}}
\newcommand{\textfour}{\dtext{Bolzano-Weierstrass:}\\\dtext{Every sequence  has a}\\\dtext{convergent subsequence}}
$
$$\fbox{$\begin{align}
&\mybox{\textone} \\ &
\begin{array}{ccccc}
\mybox{\texttwo}&\rightarrow&\mybox{\textthree}
\\&& \updownarrow 
\\ && \mybox{\textfour}
\end{array}
\end{align}$}$$

See here for why we prefer text over images when possible.

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    $\begingroup$ I agree that the OP’s example is not a compelling case (it’s basically just text, and the interrelationships aren’t particularly complicated) for posting an illustration, even as a supplement. $\endgroup$
    – ryang
    Jul 27, 2022 at 13:19
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    $\begingroup$ P.S. I do enjoy those witty mathematics comics supplementing answers. Speaking of which, it's been eons since I've come across a playful, even humorous, answer on Mathematics Stack Exchange. $\endgroup$
    – ryang
    Jul 27, 2022 at 14:01
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    $\begingroup$ @ryang, that may be because they get deleted, like this one: math.stackexchange.com/questions/73776/… $\endgroup$
    – Gerry Myerson
    Jul 27, 2022 at 23:01
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    $\begingroup$ @ryang I recently wrote answers involving Miley Cyrus and Elizabeth Taylor. They were very on-topic, and involved Markov chains and probability preserving maps. I can't say that I didn't try to integrate humor into those answers, but they remained informative and entertaining at the same time. I felt like I "lived" those answers as I wrote them. I think enough people enlivening their answers can make answers informative AND fun, even if it shouldn't be overdone. I know some users that, while they violate EoQS occasionally, wrote some very entertaining answers on this site which remain. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Jul 28, 2022 at 5:53

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