While you may be able to improve things by requiring the embedding to be smooth, you would end up with a circular definition . 2 ) A figure of 8 isn't a manifold simply because there is no open neighbourhood of the central point that is homeomorphic to the real line.
42.
The introduction has proved to be particularly dificult as its very hard to explain what addition means without very tecnical or circular definitions . 1 + 1 = 2 would seem to be the obvious article title, the current page could easily be moved to 1 + 1 = 2 ( song ).
43.
Note that " m " u is defined in terms of " A " r ( e ), and not the other way round, and so the name " electron mass in atomic mass units " for " A " r ( e ) involves a circular definition ( at least in terms of practical measurements ).
44.
If one concept is defined by another, and the other is defined by the first, this is known as a circular definition, akin to circular reasoning : neither offers enlightenment about what one wanted to know . " It is a fallacy because by using a synonym in the " definiens " the reader is told nothing significantly new ."
45.
"' [ 02 ] "'The definition I revert from, MUST be reverted from, because it is not a definition ( see definition of " circular definition " at http : / / www . sil . org / linguistics / GlossaryOfLinguisticTerms / WhatIsACircularDefinition . htm, which I again pointed out to the others at paragraph numbered "'[ 113 ] "'on the talk : libertarianism.
46.
The difference between a circular definition and a recursive definition is that a recursive definition must always have " base cases ", cases that satisfy the definition " without " being defined in terms of the definition itself, and all other cases comprising the definition must be " smaller " ( " closer " to those base cases that terminate the recursion ) in some sense.
