In article <firstname.lastname@example.org>, Tony Orlow <email@example.com> writes: > firstname.lastname@example.org wrote: >> In article <email@example.com>, Tony Orlow <firstname.lastname@example.org> writes: >>> How could anything be "flat out wrong" "without further clarification"? >>> If they aren't wrong WITH further clarification, then they aren't >>> "flat-out" wrong. Anyway.... >>> >>> A "cube" is a form where each element, a point, is connected, though an >>> edge, to n others out of a total of 2^n, such that any one can connect >>> indirectly to any other through a series of n such connections or fewer, >>> and there exists one element for each which requires exactly n such >>> connections. How's that for a definition of a square of n dimensions? :) >> >> Not good. This appears to be a partial characterization rather than >> a complete definition. >> >> I can come up with a three dimensional "cube" that fits >> this definition but which is not the same as the standard cube. >> >> Nodes A through H >> Edges AB AC AH BC BD CD DE EF EG FG FH GH >> >> Graphically >> B F >> /|\ /|\ >> --A | D--E | H-- >> \|/ \|/ >> C G >> >> 8 nodes >> Each node with 3 edges >> All interconnected using no node-to-node paths longer than 3 edges >> Each node needing at least one 3 edge path to reach at least one other node >> >> Note that in a conventional "cube", each node is a "corner" that has >> exactly one "opposite corner" that is exactly 3 edges away. > > See above, where n is the number of dimensions: > > "there exists one element for each which requires exactly n such > connections".
Note that you used "exactly n" but not "exactly one".
This implies that "one" may be read as "at least one". If you had meant "exactly one" it's clear that you knew how to phrase it.
So your definition is bad because it doesn't say what you intended for it to say.