 Posers and Puzzles

1. 19 Sep '07 22:28
a) x/x is always 1
b) dividing by 0 is not possible

What is 0/0? The two rules contadict
2. 19 Sep '07 22:301 edit
Originally posted by The Ewanator
a) x/x is always 1
b) dividing by 0 is not possible

What is 0/0? The two rules contadict
a) is not correct. You need to have a qualifier so that b) isn't a problem.

The correct expression is

x/x = 1, x =/= 0

x/x is undefined, x = 0
3. 19 Sep '07 22:32
OK, cheers, but what would you suggest as an answer to 0/0?
4. 19 Sep '07 23:40
Originally posted by The Ewanator
but what would you suggest as an answer to 0/0?
If you keep asking questions like this then I'll need to send you to l'Hopital...
5. 19 Sep '07 23:53
http://en.wikipedia.org/wiki/Division_by_zero
6. 20 Sep '07 01:361 edit
However, any function where the value x approaches a certain limit and produces a function value 0/0, can be changed or derived to a further to produce a non-zero answer.

So 0/0 can have some application.

ex.

lim (x --> 2) ((x^3)-8)/(x-2) = 0/0

((x^3)-8)/(x-2) = (x-2)(x^2+2x+4)/(x-2) = (x^2)+2x+4

lim (x--> 2) (x^2)+2x+4 = 2^2 + 2(2) + 4 = 12.
7. 20 Sep '07 01:38
Originally posted by AThousandYoung
a) is not correct. You need to have a qualifier so that b) isn't a problem.

The correct expression is

x/x = 1, x =/= 0

x/x is undefined, x = 0
You're too smart.
8. 20 Sep '07 01:49
Originally posted by Diapason
If you keep asking questions like this then I'll need to send you to l'Hopital...
🙂
9. 20 Sep '07 02:23
Originally posted by The Ewanator
OK, cheers, but what would you suggest as an answer to 0/0?
There is no answer. It's not defined.
10. 20 Sep '07 02:24
Originally posted by Ramned
You're too smart.
Thanks! 😵
11. 20 Sep '07 09:11

x^0 = 1
0^x = 1

So what is 0^0?
12. 20 Sep '07 10:031 edit
Rule #1 of math: "You shall not divide by zero!"

So if you try to divide anything with zero, even zero itself, you violate the rule #1. If you do it anyway you can get any answer, i.e. you cannot ever trust the answer.

We have a function f(x) = x/x. What is f(0)?
f(0) = 0/0 = 1 because x/x is always = 1. Right?

We have another function f(x) = 0/x. What is f(0)?
f(0) = 0/0 = 0 because 0/x is always = 0. Right?

So now I have prooved that 0/0 is both =1 and =0. Right?

Wrong. I divided by zero in both cases, thus violated rule #1, and got a unreliable result. The proofs are worthless.

Conclusion: Do not ever try to divide by zero!
13. 20 Sep '07 10:08
Originally posted by Dejection

x^0 = 1
0^x = 1

So what is 0^0?
I assume you meant:

x^0 = 1
0^x = 0 (or if you like e^x tends to 0 as e tends to 0).

So what is 0^0.

The answer is this is actually defined as being equal to 1, mainly so that the binomial theorem works!
14. 20 Sep '07 12:40
Originally posted by FabianFnas
Rule #1 of math: "You shall not divide by zero!"
It was Rule #7 the way we we're taught 🙂
15. 20 Sep '07 12:50
Originally posted by mtthw
It was Rule #7 the way we we're taught 🙂
I would love to see the six first rules of yours! 🙂