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{| align="center" cellspacing="6" width="90%" <!--QUOTE-->

{| align="center" cellspacing="6" width="90%" <!--QUOTE-->

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<p>The sum <math>x + x\!</math> generally denotes no logical term.  But <math>x,_\infty + \, x,_\infty</math> may be considered as denoting some two <math>x\!</math>'s.</p>

<p>The sum <math>x + x\!</math> generally denotes no logical term.  But <math>{x,}_\infty ~+~ {x,}_\infty</math> may be considered as denoting some two <math>x\!</math>'s.</p>

<p>It is natural to write:</p>

<p>It is natural to write:</p>

<p>We may also use the antique figures so that:</p>

<p>We may also use the antique figures so that:</p>

: <p>!2!.'x',_&infin; = `2`'x'</p>

 

<p>just as</p>

| width="25%" align="right" | <math>\mathit{2}.{x,}_\infty</math>

 

| width="10%" align="center"| <math>=\!</math>

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

| width="25%" align="left"  | <math>\mathfrak{2}x</math>

| <p>just as</p>

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

| align="center" | <math>=\!</math>

| align="left"  | <math>\mathfrak{1}</math>

<p>Then `2` alone will denote some two things.</p>

<p>Then <math>\mathfrak{2}</math> alone will denote some two things.</p>

<p>But this multiplication is not in general commutative, and only becomes so when it affects a relative which imparts a relation such that a thing only bears it to ''one'' thing, and one thing ''alone'' bears it to a thing.</p>

<p>But this multiplication is not in general commutative, and only becomes so when it affects a relative which imparts a relation such that a thing only bears it to ''one'' thing, and one thing ''alone'' bears it to a thing.</p>