Changes

<p>A subjacent number may therefore be as great as we please.</p>

<p>A subjacent number may therefore be as great as we please.</p>

<p>But all these ''ones'' denote the same identical individual denoted by w;  what then can be the subjacent numbers to be applied to 's', for instance, on account of its infinite "that is"'s?  What numbers can separate it from being identical with w?  There are only two.  The first is ''zero'', which plainly neutralizes a comma completely, since</p>

<p>But all these ''ones'' denote the same identical individual denoted by <math>\mathrm{w}\!</math>;  what then can be the subjacent numbers to be applied to <math>\mathit{s}\!</math>, for instance, on account of its infinite "''that is''"'s?  What numbers can separate it from being identical with <math>\mathrm{w}\!</math>?  There are only two.  The first is ''zero'', which plainly neutralizes a comma completely, since</p>

 

: <p>'s',_0 w = 's'w</p>

| align="center" | <math>\mathit{s},_0\!\mathrm{w} ~=~ \mathit{s}\mathrm{w}</math>

 

<p>and the other is infinity;  for as 1^&infin; is indeterminate in ordinary algbra, so it will be shown hereafter to be here, so that to remove the correlate by the product of an infinite series of 'ones' is to leave it indeterminate.</p>

<p>and the other is infinity;  for as <math>1^\infty</math> is indeterminate in ordinary algbra, so it will be shown hereafter to be here, so that to remove the correlate by the product of an infinite series of ''ones'' is to leave it indeterminate.</p>

<p>Accordingly,</p>

<p>Accordingly,</p>

 

: <p>m,_&infin;</p>

| align="center" | <math>\mathrm{m},_\infty</math>

 

<p>should be regarded as expressing 'some' man.</p>

<p>should be regarded as expressing ''some'' man.</p>

<p>Any term, then, is properly to be regarded as having an infinite number of commas, all or some of which are neutralized by zeros.</p>

<p>Any term, then, is properly to be regarded as having an infinite number of commas, all or some of which are neutralized by zeros.</p>

<p>"Something" may then be expressed by:</p>

<p>"Something" may then be expressed by:</p>

 

: <p>!1!_&infin;.</p>

| align="center" | <math>\mathit{1}_\infty\!</math>

 

<p>I shall for brevity frequently express this by an antique figure one (`1`).</p>

<p>I shall for brevity frequently express this by an antique figure one <math>(\mathfrak{1}).</math>

<p>"Anything" by:</p>

<p>"Anything" by:</p>

 

: <p>!1!₀.</p>

| align="center" | <math>\mathit{1}_0\!</math>

 

<p>I shall often also write a straight 1 for 'anything'.</p>

<p>I shall often also write a straight <math>1\!</math> for ''anything''.</p>

<p>(Peirce, CP 3.73).</p>

<p>(Peirce, CP 3.73).</p>