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I'm reading a paper in which $\circledcirc$ is used to mean an infinitesimal (from nonstandard analysis). So, for example, you would have $0<\circledcirc^2<\circledcirc$.

I'm wondering how to pronounce this symbol, and thus expressions containing it. (Zero is less than bullseye squared is less than bullseye? What's that symbol called?)

Note that I understand the name of the symbol in $\LaTeX$ (\circledcirc), but that's not what I'm asking. What does the non-standard analysis community call it when reading in their heads, or talking to students from the blackboard?

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    $\begingroup$ When your first instinct is to see if $\circledcircledcirc$ is a thing... $\endgroup$ Mar 28 '17 at 19:29
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    $\begingroup$ "donut". It really doesn't matter what it's called or what symbol is used for it, but that's short and pithy if it's necessary to be consistent with this paper. $\endgroup$
    – Kaj Hansen
    Mar 28 '17 at 19:29
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    $\begingroup$ You could also read it precisely as "rewffagag". It really doesn't matter. We use the symbol $\varepsilon$ to denote any positive number. What we really mean, though, is it's a "small" positive number. The word infinitesimal raises some suspicion, I'd steer clear from it. $\endgroup$
    – AlvinL
    Mar 28 '17 at 19:33
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    $\begingroup$ I know it's OK to say whatever I want in my own head. :) I was asking whether there is a standard that people use. If so, I'll use that in my head to get used to it. $\endgroup$
    – Nathan
    Mar 28 '17 at 19:34
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    $\begingroup$ @SimplyBeautifulArt "Standard" is a better word than "modern". $\endgroup$
    – user312097
    Mar 28 '17 at 20:16
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To answer your question: this is a non-standard symbol (perhaps appropriately in non-standard analysis); I for one have never seen it before. So it has no commonly agreed pronunciation. If the paper is well-written, it should tell you how to pronounce it; if not, you are on your own I'm afraid.

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  • $\begingroup$ OK maybe I'll get the book and see what it says, then report back here. $\endgroup$
    – Nathan
    Mar 28 '17 at 19:43
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As discussed in the comments, this is an unusual symbol. It looks kinda like a donut, and you're welcome to call it that if you like. Ultimately, notation exists to facilitate communication. If everyone knows what you're talking about then something is a good name for the symbol.

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    $\begingroup$ I'm sorry, but all I've heard so far in the comments is, "We haven't heard of this, so call it what you want." I was asking if anyone who had heard of it knew whether there was any convention for how people said it out loud. I'm asking a historical question about how people actually talk, not a philosophical question about how I'm permitted to talk. $\endgroup$
    – Nathan
    Mar 28 '17 at 19:38
  • $\begingroup$ @Nathan Well, its such a bizarre symbol you've used that we honestly don't know how to answer this. We can give you ways to say "infinitesimal" in terms of standard symbols, but we just haven't seen yours in particular. $\endgroup$ Mar 28 '17 at 19:40
  • $\begingroup$ I am content to wait for someone who has heard of the symbol. $\endgroup$
    – Nathan
    Mar 28 '17 at 19:41

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