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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 04:33, 4 May 2008
, 04:33, 4 May 2008→Note 7: trim & markup
===Note 7===
===Note 7===
One more piece of notation will save us a few bytes in the length of many of our schematic formulations.
One more piece of notation will save us a few bytes
in the length of many of our schematic formulations.
Let !X! = {x_1, ..., x_k} be a finite class of variables --
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:
quotation marks around their particular characters, though
#<p>The "(first order) differential alphabet",</p><p><math>\operatorname{d}\mathcal{X} = \{ \operatorname{d}x_1, \ldots, \operatorname{d}x_k \}.</math>
#<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>
<pre>
Before we continue with the differential analysis
Before we continue with the differential analysis
of the source proposition q, we need to pause and
of the source proposition q, we need to pause and