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Question About Limits

  1. Sep 11, 2005 #1
    I was wondering what the name for "a" is in the following example.

    The limit as x approaches a of (any function).
     
  2. jcsd
  3. Sep 11, 2005 #2

    James R

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    I don't think it has a specific name. Could be wrong, though.
     
  4. Sep 12, 2005 #3

    JasonRox

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    I don't know of any name for it either.
     
  5. Sep 12, 2005 #4

    Galileo

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    It's called "the value that x approaches".... duh :tongue2:
     
  6. Sep 12, 2005 #5

    jcsd

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    "a" would be called "a point" as in "the limit of f at a point". Of course that's not a particualrly special name.
     
  7. Sep 12, 2005 #6
    Thanks for all your replies. I was trying to word my response to a homework question last night. It doesn't really matter at all though, but I was curious.
     
  8. Sep 12, 2005 #7
    Saying "point" almost implies that the limit is equal to the value of f at that point. At least that's what I think of. "A" isn't exactly a point, it's just a value in the domain.
     
  9. Sep 12, 2005 #8

    jcsd

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    There's reason for calling it a point, a limit requires that the domain (and the range) has more structure than a primitve concept of a set; the members of the mathematical structures we require are often called points. It may almost imply something to you, but it doesn't generally as it's standard usuage.


    ps a minor quibble: "a" needn't lie in the domain of some function "f" for the limit of "f" at "a" to exist.
     
  10. Sep 12, 2005 #9

    mathwonk

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    I think it is usually named "Howard", but occasionally "Ozymandias".
     
  11. Sep 12, 2005 #10
    I see, I didn't realize this was a standard term.

    Oh yeah, I forgot about that :). I guess what I mean to say is that point implies that there is a "point" at "a" which would mean that a is in the domain of f. But you were right that if point is standard usage, then it doesn't really matter what it implies.
     
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