How do I type in special characters, such as ∞ in the terminal in vi?

While I don't know a heck of a lot about it, I have a page (somewhat dated) on Japanese in FreeBSD that, in its section on typing Romaji goes slightly into this.
http://srobb.net/jpninpt.html

Look for the section marked Romaji, towards the end of the page, it mentions the file /usr/local/lib/X11/locale/en_US_UTF-8/Compose.

Haven't tried it in years, but probably still works, though I'm not sure if that specific symbol is in there.
 
Without copying and pasting it from something else.
Which vi? vi on Linux is just a soft link to Vim. On BSDs vi is symbolic link to nvi (new vi) which is a re-implementation of the "classic Berkeley vi". "Classical Berkeley vi" has multiple versions IIRC one of which is personal copy of Bill Joy. Solaris' version of vi could also be considered classical as well as traditional vi http://ex-vi.sourceforge.net/. Reading documentation of traditional vi project is a good start. To make matters more confusing BSD projects continue to use nvi version 1.79 due to licensing issues between Berkeley Database 1.85 and the later versions by Sleepycat Software. nvi has a support for Unicode but I am not sure if the version 1.79 includes or not as I have never used Unicode with nvi. Now scottro made a major mistake mentioning Unicode as $\infty$ as written in TeX is extended Ascii character and one doesn't need Unicode to type it. I do not know how would you type $\infty$ in nvi as a professional mathematician I have never seen any mathematical symbols or mathematical text typing without serious text typing system such as TeX or Troff. TeX is de-facto standard for typing mathematics adopted since 1979 by AMS. Troff uses mathematical pre-processor and is definitely able to produce all special mathematical characters. On the web we use MathJax, a cross-browser JavaScript library that displays in web , using MathML, LaTeX and ASCIIMathML markup to write mathematics.
 
Which vi? vi on Linux is just a soft link to Vim. On BSDs vi is symbolic link to nvi (new vi) which is a re-implementation of the "classic Berkeley vi". "Classical Berkeley vi" has multiple versions IIRC one of which is personal copy of Bill Joy. Solaris' version of vi could also be considered classical as well as traditional vi http://ex-vi.sourceforge.net/. Reading documentation of traditional vi project is a good start. To make matters more confusing BSD projects continue to use nvi version 1.79 due to licensing issues between Berkeley Database 1.85 and the later versions by Sleepycat Software. nvi has a support for Unicode but I am not sure if the version 1.79 includes or not as I have never used Unicode with nvi. Now scottro made a major mistake mentioning Unicode as $\infty$ as written in TeX is extended Ascii character and one doesn't need Unicode to type it. I do not know how would you type $\infty$ in nvi as a professional mathematician I have never seen any mathematical symbols or mathematical text typing without serious text typing system such as TeX or Troff. TeX is de-facto standard for typing mathematics adopted since 1979 by AMS. Troff uses mathematical pre-processor and is definitely able to produce all special mathematical characters. On the web we use MathJax, a cross-browser JavaScript library that displays in web , using MathML, LaTeX and ASCIIMathML markup to write mathematics.

BSD's vi, to be exact.
 
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