Re: Time for a new FAQ? [ plus a tiny fraction of my ascii collection... ;) ]

Nana wrote:
> 
...
> Technically it is true that the slope of a vertical line is undefined,
> most math geeks say it has an infinite slope because...
> 
>    The formula for slope is   Rise    ( y / x )
>                              ------
>                               Run
> 
> So as x approaches 0, the slope gets larger and larger and larger,
> pretty much going off to infinity... So while it is true that the
> slope of a vertical line is undefined, the term "infinite slope" is
> used just to be more specific...

More specific, but less accurate. The slope could be getting *smaller*
and *smaller* as x approaches 0, if the line is pointing *downward* to
begin with; in that case the slope would be approaching *negative*
infinity. So when the line reaches vertical, you can argue equally well
that it has a slope of positive infinity or that it has a slope of
negative infinity, depending on which side you came from. Having two
slopes at once isn't mathematically allowed, so mathematicians rightly
say that the slope is `undefined'. (A similar thing happens for 0/0; the
answer could equally well be 0, 1, or infinity, so it's called
`undefined'.)

       ,---------------------------.
      | Wow, after all these years  |
   A  | as a boring vertical line,  |
   |  | I'm famous! I'm being       |
  _|_ | discussed in alt.ascii-art! |
  o|o  ),--------------------------'
   |  /'
   +
   |
   |
   |
   |
   V

Sorry, couldn't resist jumping on this thread. My revised a.a-a FAQ is
half-finished and will be posted in a couple of days. (More suggestions
welcome.)

-- __
  /\_\   Matthew Thomas, who does university maths (so don't argue! :-)
 _\/_/_  My real address is mpt26 @ student dot canterbury dot ac dot nz
/\_\/\_\ http://kiwipages.co.nz/matthew.html
\/_/\/_/ `Smart people think up their own quotes' -- Matthew Thomas

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