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Let <math>\mathcal{X} = \{ x_1, \ldots, x_k \}</math> be a finite class of variables, regarded as a formal alphabet of formal symbols but listed here without quotation marks.  Starting from this initial alphabet, the following items may then be defined:
 
Let <math>\mathcal{X} = \{ x_1, \ldots, x_k \}</math> be a finite class of variables, regarded as a formal alphabet of formal symbols but listed here without quotation marks.  Starting from this initial alphabet, the following items may then be defined:
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#<p>The "(first order) differential alphabet",</p><p><math>\operatorname{d}\mathcal{X} = \{ \operatorname{d}x_1, \ldots, \operatorname{d}x_k \}.</math>
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#<p>The "(first order) differential alphabet",</p><p><math>\operatorname{d}\mathcal{X} = \{ \operatorname{d}x_1, \ldots, \operatorname{d}x_k \}.</math></p>
 
#<p>The "(first order) extended alphabet",</p><p><math>\operatorname{E}\mathcal{X} = \mathcal{X} \cup \operatorname{d}\mathcal{X},</math></p><p><math>\operatorname{E}\mathcal{X} = \{ x_1, \dots, x_k, \operatorname{d}x_1, \ldots, \operatorname{d}x_k \}.</math></p>
 
#<p>The "(first order) extended alphabet",</p><p><math>\operatorname{E}\mathcal{X} = \mathcal{X} \cup \operatorname{d}\mathcal{X},</math></p><p><math>\operatorname{E}\mathcal{X} = \{ x_1, \dots, x_k, \operatorname{d}x_1, \ldots, \operatorname{d}x_k \}.</math></p>
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Before we continue with the differential analysis of the source proposition <math>q\!</math>, we need to pause and take another look at just how it shapes up in the light of the extended universe <math>\operatorname{E}X,</math> in other words, to examine in detail its tacit extension <math>\operatorname{e}q.\!</math>
    
<pre>
 
<pre>
Before we continue with the differential analysis
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of the source proposition q, we need to pause and
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take another look at just how it shapes up in the
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light of the extended universe EX, in other words,
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to examine in utter detail its tacit extension eq.
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The models of eq in EX can be comprehended as follows:
 
The models of eq in EX can be comprehended as follows:
  
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