Changes

<p>These goals can be achieved by singling out the formal language that is used by this MON to denote its set theoretic objects.  This involves separating the object domain <math>O = O_\text{MON}\!</math> from the sign domain <math>S = S_\text{MON},\!</math> paying closer attention to the naive level of set notation that is actually used by this MON, and treating its primitive set theoretic expressions as a formal language all its own.</p>

<p>These goals can be achieved by singling out the formal language that is used by this MON to denote its set theoretic objects.  This involves separating the object domain <math>O = O_\text{MON}\!</math> from the sign domain <math>S = S_\text{MON},\!</math> paying closer attention to the naive level of set notation that is actually used by this MON, and treating its primitive set theoretic expressions as a formal language all its own.</p>

</li></ol>

<p>Thus, I need to discuss a variety of formal languages on the following alphabet:</p>

Thus, I need to discuss a variety of formal languages on the following alphabet:

| <math>\underline{\underline{X}} = \underline{\underline{X}}_\text{MON} = \{ ~ {}^{\backprime\backprime} ~ {}^{\prime\prime} ~ , ~ {}^{\backprime\backprime} , {}^{\prime\prime} ~ , ~ {}^{\backprime\backprime} \{ {}^{\prime\prime} ~ , ~ {}^{\backprime\backprime} \} {}^{\prime\prime} ~ \}.\!</math>

X  =  XMON  =  { " " , "," , "{" , "}" }.

<p>Because references to an alphabet of punctuation marks can be difficult to process in the ordinary style of text, it helps to have alternative ways of naming these symbols.</p>

First, I use raised angle brackets (<...>), or "supercilia", as alternate forms of quotation marks.

First, I use raised angle brackets (<...>), or "supercilia", as alternate forms of quotation marks.