Limits: What is "a" in the Equation?

[Madeline]

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

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

 

[James R]

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

 

[JasonRox]

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

 

[Galileo]

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

 

[jcsd]

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 particularly special name.

 

[Madeline]

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.

 

[Madeline]

"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.

 

[jcsd]

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]

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

 

[Madeline]

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.