"Paul Lutus" <nospam@nosite.zzz> wrote in message news://Y58O7.115929$8q.12914143@bin2.nnrp.aus1.giganews.com...
[snip]
> If this use of "=" -- > lim x -> 0, 1/x = infinity > -- actually means "approaches infinity" and does not mean "equals infinity" > > then this use of "=" -- > > lim x -> infinity, 1/x = 0 > -- should have the same meaning: "approaches," not "equals."
But this is not the case, whether you think it should be or not.
In the second example, the LHS evaluates to a real number. The statement is asserting the equality of two real numbers.
In the first example, the LHS does not evaluate to any real number. The statement expresses the formal statement written out upthread.
> It is > disingenuous to assert a special status to the first statement that doesn't > apply to the second.
Why? They are different cases. In one the limit is defined, in the other it is not; why should they be the same?
> To assert otherwise is to say that mathematical operations and symbols mean > whatever we want them to mean, varying from context to context (even > identical ones), without regard for commonly accepted meanings
But the commonly accepted meaning *is* that a limit expression that evaluates to a real number is equal to that number (and hence *is* that number). In other words, the second statement reduces to 0 = 0, with the = sign being equality of the usual type.
> and the > desirability of unambiguous symbol usage.
There is also the desirability of appropriate generalisation. A symbol may be well used for sveral things if there is a commonality between them.
