Talk:Farey sequence: Difference between revisions

:::: "The" definition is not the only definition of a fraction, indeed, the common usage is:   a fraction if any part of a unit.   That ''any part'' may, I believe, be the ''whole part''.   Also, another point is that an ''improper fraction'' is still a fraction.   I certainly don't want to start a mathematical debate on the one true definition of a fraction --- I defer to what others have defined what a Farey sequence is (and, apparently, what it looks like) --- or, at least, how the terms are depicted --- and most important, how the end terms are depicted (defined by fiat).   Perhaps we are getting hung up on what a fraction is, rather than what a fraction looks like (or is depicted) --- at least, as far as a Farey sequence is often depicted.   Farey sequences are terms that look/appear/resemble fractions, in that there is what appears to be a numerator and a denominator, and furthermore, their equivalent values aren't used --- you don't see   '''0 .25 1/3 .5 2/3 .75 1'''   as being depicted in (or as) a Farey sequence.   It doesn't matter to me if a solidus is used or some kind of horizontal bar is between the numerator and denominator, ... as long as the Farey term ''looks'' like they are part of the Farey sequence.   Since HTML code (or plain text) is commonly used on Rosetta Code, there is nothing wrong with "plain" ASCII characters being used.   The beginning and ending terms are defined to be the value   '''0'''   and   '''1''',   denoted by the fractions (or glyphs)   '''0/1'''   and   '''1/1'''   (this is the wording the Wikipedia entry uses in its definition of a ''Farey sequence''.   Another definition that I like is the Wolfram MathWorld (TM) entry. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 07:45, 16 February 2015 (UTC)

 

 

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