Hetware wrote: >quasi wrote: >> >>On the other hand, suppose your proposed question is reworded >>in the following way ... >> >>Given: >> >> f(x) is defined and continuous for all x in R. > >I believe we can drop the "defined" since it is implied >by "continuous".
>>Then if g is defined by >> >> g(x) = limit (s -> x) f(s) >> >>can g(x) be used to determine the value of f(x) for all x in R? >> >>The answer is yes -- in fact, f(x) = g(x) for all x in R. > >What is your opinion of the definition given as follows: > >Let f(x) be continuous over R, and f(x) = x/x for all x in R >where x/x is a determinate form?
I wouldn't use the phrase:
"where x/x is a determinate form"
"where x/x is defined"
You could also say it more simply this way:
"Let f be a function which is continuous over R and such that f(x) = x/x for x != 0."
Or even simpler:
"Let f(x) = 1.
But at this point, you surely understand the terminology and conventions relating to this issue as used in the text by Thomas. Why not just go on from there?