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Madeline

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The limit as x approaches

__a__of (any function).

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- Thread starter Madeline
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- #1

Madeline

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The limit as x approaches

- #2

James R

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I don't think it has a specific name. Could be wrong, though.

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JasonRox

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I don't know of any name for it either.

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Galileo

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It's called "the value that x approaches"... *duh* :tongue2:

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jcsd

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Madeline said:

The limit as x approachesaof (any function).

"a" would be called "a point" as in "the limit of f at a point". Of course that's not a particularly special name.

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Madeline

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- #7

Madeline

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jcsd said:"a" would be called "a point" as in "the limit of f at a point". Of course that's not a particularly special name.

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.

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jcsd

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Madeline said: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.

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.

- #9

mathwonk

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I think it is usually named "Howard", but occasionally "Ozymandias".

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Madeline

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jcsd said: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.

I see, I didn't realize this was a standard term.

ps a minor quibble: "a" needn't lie in the domain of some function "f" for the limit of "f" at "a" to exist.

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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