1. ## Division Result

What would be the result of the following divisions?

Code:
```a. 1/0
b. 1/INFINITY
c. INFINITY/0
d. 0/INFINITY
e. INFINITY/1
f. INFINITY/INFINITY
g. 0/0```

2. Negative infinity - 42. Obviously.

3. Code:
```#include <stdio.h>
#include <math.h>
int main(void) {
float a = 1.0f;
float b = 0.0f;
float c = INFINITY;
printf("%f %f %f %f %f %f %f\n", a/b, a/c, c/b, b/c, c/a, c/c, b/b);
return 0;
}```
C99 at least is guaranteed to follow IEEE guidelines.

4. Are you asking with respect to the rules of some branch of mathematics or a programming language?

5. a. undefined
b. nearly zero
c. undefined
d. zero
e. infinity
f. 1
g.undefined (I think)

6. Originally Posted by psychopath
a. undefined
b. nearly zero
c. undefined
d. zero
e. infinity
f. 1
g.undefined (I think)
I'll give you 3.5/7 for that (at least as far as real analysis goes).

7. Trying to remember from calc 2 (it has been awhile and was probably the least useful semester) but isn't the division by inf indeterminate? IIRC you can talk about a variable as it approaches infinity but you can't use infinity as a number.

8. Originally Posted by laserlight
Are you asking with respect to the rules of some branch of mathematics or a programming language?
This would be a critical question to get an answer to, as there is sometimes a significant difference between theoretical math and how a computer performs under those circumstances. Although I'm sure that both normally treat x/0 as "division by zero", where this normally leads to a hardware exception in a computer [so it stops the application] (but this is also usually configurable).

As so often is the case, the question is not clear enough in it's scope to give a complete answer.

--
Mats

9. Originally Posted by Thantos
IIRC you can talk about a variable as it approaches infinity but you can't use infinity as a number.
In B I believe you would have to say that limit is zero as infinity is approached. But in D I was under the impression that whether you can treat infinity as a number or not, zero divided by anything had to be zero. And in F, anything divided by itself was always one.

I could be completely wrong though. Only one year of precalc under my belt .

10. Well, for f, consider (x^2)/x. Both go to infinity as x gets large, but the quotient is still infinity. (And of course, you can go the other way to get a quotient of zero, which is why f is undefined.)

11. I don't think f is undefined but is indeterminate. I gotta dig out the book I think

12. And really since all but two are talking about infinity I have to assume that really means that as the function approaches some value it goes towards infinity. With the 0 it really depends if you mean:

x / 0
or
x/f(y) as y approaches some number that causes f(y) to approach 0.

13. Originally Posted by Thantos
I don't think f is undefined but is indeterminate. I gotta dig out the book I think
Same thing (or at least I meant by undefined what you mean by indeterminate).

14. I always thought that infinity is not a number, but a process, so an expression like 1/infinity is invalid and meaningless. You can express it as a limit, however, as in "(lim x->inf) 1/x". In that case, it's asking what value does 1/x approach as x approaches infinity. The answer would be 0.

Anything divided by zero is undefined. "(lim x->0+) 1/x", though, is +inf, whereas "(lim x->0-) 1/x", is -inf.

I have only taken one calculus course, though (AP calculus. graduating highschool this year ), so correct me if I'm wrong.

15. Originally Posted by cyberfish
Anything divided by zero is undefined. "(lim x->0+) 1/x", though, is +inf, whereas "(lim x->0-) 1/x", is -inf.
You can't have your cake and eat it too. What you say is not true when limits come into the picture. For example, the limit as x->0 of (x/x) is 1. Many basic results of differential calculus are based on such limits being defined.