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Infinity is defined as something that is uncountable. But every where I see the symbol of Infinity as a closed loop. My professor said, that it symbolizes that the boundary of Infinity is determined but it isn't so. I too agree with him. The Infinity symbol must be open curve rather than closed, something like this:
enter image description here
I would like to define and use this symbol for Infinity. How do I achieve it?

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    I can't agree with your professor's opinion. This symbol doesn't denote infinity when referred to sets, but just a mathematical concept used in analysis. – egreg Jul 23 '14 at 13:59
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    If you want to be understood by other mathematicians, use established symbols. Or do you also write ":" instead of "2" because the colon better represents two-hood? --That beng said, you might add a small white blob on top of the standard $\infty$ symbol (assuming you only write on white background) – Hagen von Eitzen Jul 23 '14 at 14:22
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    Adding infinity gives a one-point compactification of the real numbers, which the closed shape nicely suggests. – Mass Jul 23 '14 at 15:46
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    I agree with @egreg (and not with your professor). It is just a symbol used traditionally. – user11232 Jul 25 '14 at 2:28
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    I like that you're trying to capture intuition by changing notation, but this seems too specific to a certain interpretation. Also, you shouldn't expect to capture a symbol's meaning so specifically by how it's written. You could say $\infty$ is special in that it only ever means infinity. But on that route, why not take issue with it having an intersection point? Why doesn't $O$ mean infinity? Hmm, then what would we do about $0$? I think it's worth living with some counterintuitive notation for the sake of universal communication. – j0equ1nn Apr 25 '17 at 10:51
6

Both symbols are available in Unicode:

  • U+221D: ∝ PROPORTIONAL TO
  • U+221E: ∞ INFINITY

It is not a good idea to replace the well-established symbol for infinity, which even many non-mathematicians will understand, by a different symbol, a relational operator, which is used for a complete different purpose. This is called obfuscating and will irritate the user at best.

Of course LaTeX can print both symbols:

\documentclass{article}
\usepackage{amsfonts}% or latexsym, amssymb, mathabx, txfonts, pxfonts, wasysym
\begin{document}
\[ \infty \propto \]
\end{document}

Result

If \propto is used as symbol for infinity, then it needs a set of curly braces to get rid of the \mathrel property, e.g.:

\newcommand*{\myinfinity}{{\propto}}

Example for LuaTeX/XeTeX with Unicode math fonts. The example also shows different input methods for the symbols:

\documentclass{article}
\usepackage{unicode-math}
\begin{document}
\noindent
% Latin modern
\[ \infty \propto \]
\setmathfont{Asana-Math.otf}
\[ ∞ ∝ \]
\setmathfont{xits-math.otf}
\[ ∞ ∝ \]
\setmathfont{texgyrepagella-math.otf}
\[ ^^^^221e ^^^^221d \]
\end{document}

Result LuaTeX/XeTeX

  • Ugh, no, don't use \propto. It already means proportional to. That would be horribly confusing. – EL_DON Jul 26 '17 at 16:55
  • @EL_DON \propto is just the macro name as provided by the packages, no more, no less. – Heiko Oberdiek Jul 26 '17 at 17:50
  • To clarify, don't use the proportional symbol for infinity. You may as well use 4 as a symbol for 3. – EL_DON Jul 26 '17 at 22:11
  • @EL_DON Then the comment belongs to the question. Only the OP and the professor of the OP want to use the proportional symbol for infinity. The first paragraph of the answer, however, votes against the off-label usage. – Heiko Oberdiek Jul 26 '17 at 23:25
  • Other answers made an infinity symbol with a notch cut out with a white mark. While still confusing, that method answers the question without reusing another symbol exactly. – EL_DON Jul 27 '17 at 14:12
3

You can create your own copy of used math font and you can do changes here by fontforge program, for example.

Or you can redefine the \infty macro, for example by such way:

\let\oriinfty=\infty
\def\infty{{\oriinfty\llap{\vrule height.24em depth-.2em width.2em}}}

This example does the black rule over the infinity char in the appropriate place. Now, it is your exercise to do this rule not black but white. You can use color or xcolor package and set the color statement for the \llap{...} part of my macro.

It is more complicated to do this working in scriptstyle and scripscriptstyle too. Read the documentation about \mathchoice TeX primitive for this.

Note: I don't evaluate here if this is good or bad decision to change the infinity character.

3
\documentclass{article}
\usepackage{color}
\newcommand\myinfty{{\infty%
\mathchoice%
{\llap{\color{white}\vrule width 0.2em height 0.3em depth -0.15em}}%
{\llap{\color{white}\vrule width 0.2em height 0.3em depth -0.15em}}%
{\llap{\color{white}\vrule width 0.2em height 0.22em depth -0.1em}}%
{\llap{\color{white}\vrule width 0.2em height 0.15em depth -0.09em}}%
}}
\begin{document}  
In Text: $\sum_{n=1}^\myinfty \frac1n = \myinfty$
and $\myinfty_{\myinfty_\myinfty}^{\myinfty^\myinfty} $.
In display:
\[\sum_{n=1}^\myinfty \frac1n = \myinfty\]
\[\myinfty_{\myinfty_\myinfty}^{\myinfty^\myinfty}\]
\end{document}
  • I took the liberty of removing the pdftex option to color, which shouldn't be given; also I changed $$...$$ into the more correct \[...\]. And +1. – egreg Jul 23 '14 at 14:56

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