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

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

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<p>Addition being taken in this sense, ''nothing'' is to be denoted by ''zero'', for then:</p>

<p>Addition being taken in this sense, ''nothing'' is to be denoted by ''zero'', for then</p>

 

: <p>''x'' +, 0 = ''x''</p>

| align="center" | <math>x ~+\!\!,~ 0 ~=~ x</math>

 

<p>whatever is denoted by ''x'';  and this is the definition of ''zero''.  This interpretation is given by Boole, and is very neat, on account of the resemblance between the ordinary conception of ''zero'' and that of nothing, and because we shall thus have</p>

 

<p>whatever is denoted by <math>x\!</math>;  and this is the definition of ''zero''.  This interpretation is given by Boole, and is very neat, on account of the resemblance between the ordinary conception of ''zero'' and that of nothing, and because we shall thus have</p>

: <p>[0] = 0.</p>

 

| align="center" | <math>[0] ~=~ 0.</math>

<p>(Peirce, CP 3.67).</p>

<p>(Peirce, CP 3.67).</p>

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With respect to the nullity 0 in ''S'' and the number 0 in '''R''', we have:

With respect to the nullity <math>0\!</math> in <math>S\!</math> and the number <math>0\!</math> in <math>\mathbb{R},</math> we have:

: ''v''0 = [0] = 0.

| <math>v0 ~=~ [0] ~=~ 0.</math>

In sum, therefor, it also serves that only preserves a due respect for the function of a vacuum in nature.

In sum, therefore, it also serves that only preserves a due respect for the function of a vacuum in nature.

===Commentary Note 11.20===

===Commentary Note 11.20===