Changes

<p>'''The Signs of Inclusion, Equality, Etc.'''</p>

<p>'''The Signs of Inclusion, Equality, Etc.'''</p>

<p>I shall follow Boole in taking the sign of equality to signify identity.  Thus, if v denotes the Vice-President of the United States, and p the President of the Senate of the United States,</p>

<p>I shall follow Boole in taking the sign of equality to signify identity.  Thus, if <math>v\!</math> denotes the Vice-President of the United States, and <math>p\!</math> the President of the Senate of the United States,</p>

 

<p>v = p</p>

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

 

<p>means that every Vice-President of the United States is President of the Senate, and every President of the United States Senate is Vice-President.</p>

<p>means that every Vice-President of the United States is President of the Senate, and every President of the United States Senate is Vice-President.</p>

<p>The sign "less than" is to be so taken that</p>

<p>The sign "less than" is to be so taken that</p>

 

<p>f &lt; m</p>

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

 

<p>means that every Frenchman is a man, but there are men besides Frenchmen.</p>

<p>means that every Frenchman is a man, but there are men besides Frenchmen.</p>

<p>Drobisch has used this sign in the same sense.  It will follow from these significations of '=' and '<' that the sign '-<' (or '=<', "as small as") will mean "is".  Thus,</p>

<p>Drobisch has used this sign in the same sense.  It will follow from these significations of <math>=\!</math> and <math><\!</math> that the sign <math>-\!\!\!<\!</math> (or <math>\leqq,</math> "as small as") will mean "is".  Thus,</p>

 

<p>f -< m</p>

| align="center" | <math>f -\!\!\!< m</math>

 

<p>means "every Frenchman is a man", without saying whether there are any other men or not.  So,</p>

<p>means "every Frenchman is a man", without saying whether there are any other men or not.  So,</p>

 

<p>'m' -< 'l'</p>

| align="center" | <math>m -\!\!\!< l</math>

 

<p>will mean that every mother of anything is a lover of the same thing;  although this interpretation in some degree anticipates a convention to be made further on.  These significations of '=' and '<' plainly conform to the indispensable conditions.  Upon the transitive character of these relations the syllogism depends, for by virtue of it, from</p>

<p>will mean that every mother of anything is a lover of the same thing;  although this interpretation in some degree anticipates a convention to be made further on.  These significations of <math>=\!</math> and <math><\!</math> plainly conform to the indispensable conditions.  Upon the transitive character of these relations the syllogism depends, for by virtue of it, from</p>

<p>f -< m</p>

<p>f -< m</p>