Quantifier is too small next to dfrac

Question

I want to work with fractions, quantifying a fraction as single element, but \forall and \exists are being displayed too small near \dfrac. And mathlarger doesn't seem to work.

I know only the basics of latex and haven't found anything that resolves this problem.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{relsize}
\begin{document}
    \begin{enumerate}
        \item Neutral: $\mathlarger{\exists!} \dfrac{x}{y} : \dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}$
    \end{enumerate}
\end{document}

What about 2\cdot\dfrac{1}{3}? Would you think that the 2 is too small? — egreg, Oct 24 '22 at 09:04
No, the number 2 is not small, 1 and 3 are natural numbers and so 2, it makes sense all have the same size. But the quantifier seems to me that he should have the same size of what follows. — Mateus Schroeder da Silva, Oct 24 '22 at 09:09
I see no reason to. By the way, what would \exists \frac{x}{y} mean? — egreg, Oct 24 '22 at 09:10
Have you seen any published math texts that expand quantifiers in that way? As egreg hints they are usually set as normal characters in the current font size — David Carlisle, Oct 24 '22 at 09:11
@egreg The op possibly means "there is only one \dfrac{x}{y} such that \dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}" in which \exists! means "there is only one". — M. Logic, Oct 24 '22 at 09:15
Let me suggest another solution: Replace the quantifier by “There exists...”. Quantifiers and implication arrows don’t really add any benefit to the text. Too much notation just makes the text unnecessarily heavy for the reader. — Gaussler, Oct 24 '22 at 09:15
You can try \scalebox{1.2}{$\exists!$} by \usepackage{graphicx} if you want mathlarger. See here. — CCCCCC666666, Oct 24 '22 at 09:18
@M.Logic The existential quantifier applies to variables. Denoting a variable by \dfrac{x}{y} isn't a good choice, in my opinion. I endorse Gaussler's idea of using words, rather than difficult to interpret (and out of place) logical symbols. — egreg, Oct 24 '22 at 09:19
@egreg Actually, if I had to pick an element in a field of fractions, I could very well find myself writing “Let x/y be an element”. But I would never write “∃ x/y”, except perhaps on the blackboard when teaching. — Gaussler, Oct 24 '22 at 09:22
@egreg It was intended to show the nature of the number I am working on, an ordered pair of integers, with that notation. But I understand what you said, it didn't look so weird when I thought it first time. — Mateus Schroeder da Silva, Oct 24 '22 at 11:04
@Gaussler yes, it is a good point but I fear being too repetitive. (on the context i'm working) — Mateus Schroeder da Silva, Oct 24 '22 at 11:07
@egreg \exists!\drac{x}{y}\phi(\dfrac{x}{y}) could be seen as a shorthand for \exists!z(z=\dfrac{x}{y}\wedge\phi(z)). — M. Logic, Oct 25 '22 at 04:13
@DavidCarlisle In my opinion, any kind use of symbols should be permitted as long as (1) the meaning of such use is clear, (2) such use won't bring any problems, and (3) such use is accordance with people's usual tastes on symbols. — M. Logic, Oct 25 '22 at 11:32
@DavidCarlisle No, you didn't say that clearly, and so it may be my mistake. — M. Logic, Oct 25 '22 at 11:36
@M.Logic the question wording was more about typographic judgement than what is allowed, "are being displayed too small " could be rephrased as "following standard conventions" — David Carlisle, Oct 25 '22 at 11:40
@DavidCarlisle More precisely, "how to get larger \exists! appropriately". By the way, \exists! in the usual size is my personal taste. — M. Logic, Oct 25 '22 at 11:48

M. Logic · Accepted Answer · 2022-10-25T04:40:28.060

Perhaps what you need is a symbol which acts like a large operator. See the following codes and output.

\documentclass{article}
\usepackage{amsmath}
\usepackage{scalerel}
\makeatletter
\DeclareMathOperator*{\bigexistsone}{\scalerel*{\exists!}{\sum}}
\makeatother
\begin{document}
\begin{enumerate}
\item The original one in text style in lines: $\exists!\dfrac{x}{y}\left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right)$, and the new one in display style between lines: $$\exists!\dfrac{x}{y}\left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right).$$
\item The new one in text style in lines: $\bigexistsone\dfrac{x}{y}\left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right)$, and the new one in display style between lines: $$\bigexistsone\dfrac{x}{y} \left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right).$$
\end{enumerate}
\end{document}

Quantifier is too small next to dfrac

1 Answers1