Question About Limits

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I was wondering what the name for "a" is in the following example.

The limit as x approaches a of (any function).
 

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James R
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I don't think it has a specific name. Could be wrong, though.
 
JasonRox
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I don't know of any name for it either.
 
Galileo
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It's called "the value that x approaches".... duh :tongue2:
 
jcsd
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Madeline said:
I was wondering what the name for "a" is in the following example.

The limit as x approaches a of (any function).
"a" would be called "a point" as in "the limit of f at a point". Of course that's not a particualrly special name.
 
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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.
 
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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 particualrly 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.
 
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.
 
mathwonk
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I think it is usually named "Howard", but occasionally "Ozymandias".
 
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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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