Changes

by the following equations:

by the following equations:

<pre>

<br><font face="courier new">

o-------------------------------------------------o

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|                                                 |

|         u'   =   u + du  =   (u, du)           |

{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:center; width:96%"

|                                                 |

| &nbsp; || ''u''’ || = || ''u'' + d''u'' || = || (''u'', d''u'') || &nbsp;

|         v'   =   v + du  =   (v, dv)           |

|                                                 |

| &nbsp; || ''v''’ || = || ''v'' + d''u'' || = || (''v'', d''v'') || &nbsp;

|}

</pre>

|}

</font><br>

These relations correspond to the formal substitutions that are made in defining E''J'' and D''J''.  For now, the whole rigamarole of contingency spaces can be regarded as a technical device for achieving the effect of these substitutions, adapted to a setting where functional compositions and other symbolic manipulations are difficult to contemplate and execute.

These relations correspond to the formal substitutions that are made in defining E''J'' and D''J''.  For now, the whole rigamarole of contingency spaces can be regarded as a technical device for achieving the effect of these substitutions, adapted to a setting where functional compositions and other symbolic manipulations are difficult to contemplate and execute.