# Thread: Product with undefined term

1. Let c=ab. Assume b is undefined (but bounded). If a=0, is c=0 or is c undefined?  2.

3. Originally Posted by mathman Let c=ab. Assume b is undefined (but bounded). If a=0, is c=0 or is c undefined?
While one could make a reasonable argument for c=0, I'm going with c is undefined.

EDIT: However, if an inequality that specifies the bound is provided, then b is no longer undefined and it can be proven that c=0.  4. Case of interest f(x)=xsin(1/x). c=f(0).  5. Originally Posted by mathman Case of interest f(x)=xsin(1/x). c=f(0).
I think the goal posts are moved here though, the first equation is algebraic (and b is implicitly some element of a semigroup at least?) while the second is asking something about limits?  6. Originally Posted by river_rat  Originally Posted by mathman Case of interest f(x)=xsin(1/x). c=f(0).
I think the goal posts are moved here though, the first equation is algebraic (and b is implicitly some element of a semigroup at least?) while the second is asking something about limits?
a and b are numbers. In the example a=0 while b=sin(1/0).  7. Originally Posted by mathman b=sin(1/0).
That isn't a number though?

We could consider a linear function space and a functional where we evaluate at x=0, but then sin(1/x) is not an element or the functional is not defined for all elements of the space. Domains matter for questions like this.  Bookmarks
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