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Symbolic notation

I just love teaching Calculus. I have a hard time seeing why something like the following mathematical definition is not met with cheers of adulation for its specificity and conciseness. It says so much with so little and can be taken so far.

 a_n \rightarrow L \ \mbox{\ as \ } \  n \rightarrow \infty \iff  \ \forall \varepsilon &gt; 0 \ \exists \ N \in \mathbb{Z}^+ \ \mbox{s.t.} \ n \geq N \Rightarrow | a_n - L | < \varepsilon

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5 Responses to “Symbolic notation”

  1. on 11 Oct 2005 at 12:18 pm mommyfranklin

    You nerd!
    Let’s see if I remember what all that stuff means — A sub n approaches L as n approaches infinity for every epsilon greater than 0 there exists an integer such that ….

    Nope I don’t remember…

  2. on 11 Oct 2005 at 2:12 pm SplineGuy

    Just in case you are curious. Here is a translation (not that it makes any more simple):

    “a sub n approaches L as n approaches infinity if and only if for every epsilon greater that zero, there exists a positive integer N such that if n is greater than or equal to N then a sub n is within epsilon of L”

    (beautiful)

  3. on 18 Oct 2005 at 7:15 am jonboy

    “Beauty is in the eye of the beholder.”

  4. on 18 Oct 2005 at 12:38 pm SpookyRach

    Beauty is only spline deep.

  5. on 19 Oct 2005 at 9:12 pm N'ida

    beauty is only skin deep, but UGLY goes clear to the bone.

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