Changes

Grammar&nbsp;1 is something of a misnomer.  It is nowhere near exemplifying any kind of a standard form and it is only intended as a starting point for the initiation of more respectable grammars.  Such as it is, it uses the terminal alphabet <math>\mathfrak{A} = \mathfrak{M} \cup \mathfrak{P}</math> that comes with the territory of the cactus language <math>\mathfrak{C} (\mathfrak{P}),</math> it specifies <math>\mathfrak{Q} = \emptyset,</math> in other words, it employs no intermediate symbols, and it embodies the ''covering set'' <math>\mathfrak{K}</math> as listed in the following display.

Grammar&nbsp;1 is something of a misnomer.  It is nowhere near exemplifying any kind of a standard form and it is only intended as a starting point for the initiation of more respectable grammars.  Such as it is, it uses the terminal alphabet <math>\mathfrak{A} = \mathfrak{M} \cup \mathfrak{P}</math> that comes with the territory of the cactus language <math>\mathfrak{C} (\mathfrak{P}),</math> it specifies <math>\mathfrak{Q} = \emptyset,</math> in other words, it employs no intermediate symbols, and it embodies the ''covering set'' <math>\mathfrak{K}</math> as listed in the following display.

{| align="center" cellpadding="10" cellspacing="0" width="90%"

{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"

|-

| align="left" style="border-left:1px solid black;"  width="33%" |

| width="90%" style="border-top:1px solid black; border-left:1px solid black;"  |

<math>\mathfrak{C} (\mathfrak{P})</math>

<math>\mathfrak{C} (\mathfrak{P}).\ \text{Grammar 1}</math>

| width="10%" style="border-top:1px solid black; border-right:1px solid black;" |

<math>\text{Grammar 1}\!</math>

| align="right" style="border-right:1px solid black;" width="33%" |

<math>\mathfrak{Q} = \emptyset</math>

<math>\mathfrak{Q} = \emptyset</math>

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|-

| colspan="2" style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black;" |

| colspan="3" style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black" |

<math>\begin{array}{llll}

<math>\begin{array}{llll}

1. & S & :> & m_1 \ = \ ^{\backprime\backprime} \operatorname{~} ^{\prime\prime} \\

1. & S & :> & m_1 \ = \ ^{\backprime\backprime} \operatorname{~} ^{\prime\prime} \\