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This is an extremely small distance insignificant for the precision of your theme. It represents the minimum distance between Nodes. ET uses the Fuzzy Tolerance to clean the theme and to keep the Polyline topology. If nodes are found closer to each other than the Fuzzy Tolerance they are moved to form one node.  All the features with length smaller than this tolerance are considered redundant.  The default tolerance is 0.000001  * (W + H ) / 2: where W is the width and H is the Height of the the extent of the editing theme. If the editing theme has extents 1km/1km the default tolerance will be 1mm. The MIN tolerance the user can set is 0.000000001* (W + H ) / 2. The MAX tolerance can be   0.00001* (W + H ) / 2.
The smaller the value of Fuzzy Tolerance is, the bigger is the possibility of encountering PseudoPseudo Nodes. If the value of the tolerance is close to the MAX value some undesirable result might occur.

ARC/INFO uses Fuzzy Tolerance for many procedures - Clean, Intersect etc., but it has not been implemented in ArcView. If you use ArcView standard split tool to split a Polyline and then analyze the nodes (you can use ET, ET-Demo or any other script or extension which does that) in many cases you will see picture like this:ppnodes1.jpg (9034 bytes). The definition of Pseudo node is "Pseudo nodes occur where a single line connects with itself  or where only two Polylines intersect.". Why then we have here Pseudo nodes where four Polylines intersect?   The answer is in the next picture. If you zoom in enough you will see something similar to this: ppnodes2.jpg (1705 bytes) Actually the four arcs do not intersect in one point. In fact two of them do not intersect at all. The distance between the two Pseudo nodes in my example is      4.58286*E-13. OK ArcView does not have problem with the lack of actual intersection. If you use Network Analyst to find the best route it will find it like this: ppnodes3.jpg (3304 bytes). This does not harm at all because the distance difference is almost nothing. However if you want to perform some cleaning exercise on your data it can cost you a LOT.

This phenomenon (most probably caused by ArcView's single precision numbers and the lack of Fuzzy Tolerance) I called PseudoPseudo Nodes and this is the term I'm using in ET. If you are sometimes frustrated from the speed of cleaning procedure, know that half of it is because of PseudoPseudo Nodes.