text: # [Haskell-cafe] Re: 0/0 > 1 == False
  
  Jonathan Cast jonathanccast at fastmail.fm
  Sun Jan 13 19:21:59 EST 2008
  
  ```On 12 Jan 2008, at 3:33 AM, Cristian Baboi wrote:
  
  > On Sat, 12 Jan 2008 13:23:41 +0200, Kalman Noel
  > <kalman.noel at bluebottle.com> wrote:
  >
  >> Achim Schneider wrote:
  >>> Actually, lim( 0 ) * lim( inf ) isn't anything but equals one, and
  >>> the anything is defined to one (or, rather, is _one_ anything) to be
  >>> able to use the abstraction. It's a bit like the difference between
  >>> eight pens and a box of pens. If someone knows how to properly
  >>> formalise n = 1, please speak up.
  >>
  >> Sorry if I still don't follow at all.  Here is how I understand
  >> (i. e.
  >> have learnt) lim notation, with n ∈ N, a_n ∈ R.  (Excuse my poor
  >> terminology, I have to translate this in my mind from German maths
  >> language ;-).  My point of posting this is that I don't see how to
  >> accommodate the lim notation as I know it with your term. The
  >> limit of
  >> infinity?  What is the limit of infinity, and why should I
  >> multiplicate
  >> it with 0?  Why should I get 1?
  >>
  >>     (1) lim a_n  = a                (where a ∈ R)
  >>     (2) lim a_n  = ∞
  >>     (3) lim a_n  = − ∞
  >>     (4) lim { x → x0 } f(x) = y     (where f is a function into R)
  >>
  >>     (1) means that the sequence of reals a_n converges towards a.
  >>
  >>     (2) means that the sequence does not converge, because you can
  >>         always find a value that is /larger/ than what you hoped
  >> might
  >>         be the limit.
  >>    (3) means that the sequence does not converge, because you can
  >>         always find a value that is /smaller/ than what you hoped
  >> might
  >>         be the limit.
  >>
  >>     (4) means that for any sequence of reals (x_n ∈ dom f)
  >> converging
  >>         towards x0, we have lim f(x_n) = y.  For this equation
  >> again, we
  >>         have the three cases above.
  >
  > Suppose lim a_n = a , lim b_n = b, c_2n = a_n, c_2n+1 = b_n.
  >
  > What is lim c_n ?
  
  If a = b, lim c_n = a = b.  Otherwise lim c_n is undefined, in the
  sense that there is no number c such that the assertion lim c_n = c
  is true.  The `=' in this assertion isn't an equality; it's just a
  bit of math syntax, used in the special case where it isn't overly
  confusing.
  
  jcc
  
  ```
explanation: The text is an email thread discussing mathematical concepts, specifically limits and sequences. It contains a question about the limit of a sequence that alternates between two converging sequences. There is no provided answer to this specific question within the text.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # [Haskell-cafe] Re: 0/0 > 1 == False
  
  Jonathan Cast jonathanccast at fastmail.fm
  Sun Jan 13 19:21:59 EST 2008
  
  ```On 12 Jan 2008, at 3:33 AM, Cristian Baboi wrote:
  
  > On Sat, 12 Jan 2008 13:23:41 +0200, Kalman Noel
  > <kalman.noel at bluebottle.com> wrote:
  >
  >> Achim Schneider wrote:
  >>> Actually, lim( 0 ) * lim( inf ) isn't anything but equals one, and
  >>> the anything is defined to one (or, rather, is _one_ anything) to be
  >>> able to use the abstraction. It's a bit like the difference between
  >>> eight pens and a box of pens. If someone knows how to properly
  >>> formalise n = 1, please speak up.
  >>
  >> Sorry if I still don't follow at all.  Here is how I understand
  >> (i. e.
  >> have learnt) lim notation, with n ∈ N, a_n ∈ R.  (Excuse my poor
  >> terminology, I have to translate this in my mind from German maths
  >> language ;-).  My point of posting this is that I don't see how to
  >> accommodate the lim notation as I know it with your term. The
  >> limit of
  >> infinity?  What is the limit of infinity, and why should I
  >> multiplicate
  >> it with 0?  Why should I get 1?
  >>
  >>     (1) lim a_n  = a                (where a ∈ R)
  >>     (2) lim a_n  = ∞
  >>     (3) lim a_n  = − ∞
  >>     (4) lim { x → x0 } f(x) = y     (where f is a function into R)
  >>
  >>     (1) means that the sequence of reals a_n converges towards a.
  >>
  >>     (2) means that the sequence does not converge, because you can
  >>         always find a value that is /larger/ than what you hoped
  >> might
  >>         be the limit.
  >>    (3) means that the sequence does not converge, because you can
  >>         always find a value that is /smaller/ than what you hoped
  >> might
  >>         be the limit.
  >>
  >>     (4) means that for any sequence of reals (x_n ∈ dom f)
  >> converging
  >>         towards x0, we have lim f(x_n) = y.  For this equation
  >> again, we
  >>         have the three cases above.
  >
  > Suppose lim a_n = a , lim b_n = b, c_2n = a_n, c_2n+1 = b_n.
  >
  > What is lim c_n ?
  
  If a = b, lim c_n = a = b.  Otherwise lim c_n is undefined, in the
  sense that there is no number c such that the assertion lim c_n = c
  is true.  The `=' in this assertion isn't an equality; it's just a
  bit of math syntax, used in the special case where it isn't overly
  confusing.
  
  jcc
  
  ```
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text is an email thread discussing mathematical concepts, specifically limits and sequences. It contains a question about the limit of a sequence that alternates between two converging sequences. There is no provided answer to this specific question within the text.
  
  Label: question