This is really a math question, so it evokes my old math-major traits- mainly pickiness.
Math questions really require some precision before they can be answered.
Here, I'm not quite sure what you mean by 'infinity' as a noun.
I definitely have no idea what you mean by the verb 'covers'.
So perhaps it would be possible to rephrase the question using
terms whose meaning can be explained. In the process, you might
discover the answer yourself. Meanwhile, I'm clueless.
Mike W.
I'm having a bit of trouble with "large" and "small" as well, but
only in a trivial sense -- I think of large, negative numbers as large,
but less than negative numbers of less absolute value.
"Infinity" is usually just shorthand for a process of taking a
limit with a finite number as an input, and observing how something
changes as that input number gets larger and larger. Sometimes the
limit of the same function as the input parameter gets more and more
negative is very different. Consider the function f(x)=Arctan(x). The
limit of f(x) as x goes to infinity is pi/2, while the limit of f(x) as
x goes to negative infinity is -pi/2, so in this restricted application
these are different. If x can be complex, then f(x) has no limit as x
goes to infinity; Arctan(x) has an essential singularity at infinity in
the complex plane, so it doesn't take much to make this argument break
down.
Tom
(published on 10/22/2007)
