1. ## Nothing

Can you make 120 using only five 0's?

You may use any and as many mathematical operators as you want to achieve the task.

2. ## Re: Nothing

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The exclamation mark seems to be the deciding factor!</span hide>

3. ## Re: Nothing

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> Indeed</span hide>

I'll let the others provide me with the solution <img src=/S/evilgrin.gif border=0 alt=evilgrin width=15 height=15>

4. ## Re: Nothing

For those who need their <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">"exclamations"</span hide> and excitement more specific:
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">(0!+0!+0!+0!+0!)!</span hide>

Steve

5. ## Re: Nothing

I can do it using just two zeros:

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">0

6. ## Re: Nothing

Steve/Hans

<img src=/S/trophy.gif border=0 alt=trophy width=15 height=15>

7. ## Re: Nothing

OK Alan, you've stumped me

How?

8. ## Re: Nothing

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">0 divided by 0 is undefined - it can be anything: 37, or 120, or -3.141592, or ...</span hide>

9. ## Re: Nothing

Thanks Hans

I thought Alan was doing it using a trickery with bases <img src=/S/bash.gif border=0 alt=bash width=35 height=39>

10. ## Re: Nothing

It's actually described as <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">indeterminate</span hide> rather than <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">undefined</span hide>.
The latter is used to describe quantities of <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">infinite or infinitesimal magnitudes</span hide> while the former includes <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">"tenable" quantities whose values can not be determined from the available information alone</span hide>.

Alan

11. ## Re: Nothing

Well, that's told us then! <img src=/S/dizzy.gif border=0 alt=dizzy width=15 height=15>

12. ## Re: Nothing

It's not that hard to visualize actually. If I define a function as:
f(x) = 2x * (x-60) / (x-60)
then it has the value "2x" for all values of x, except for x=60, in which case it has a value of 0/0. If you graph the function, excluding just the 0/0 value, you'll see that the 0/0 "anomoly" occurs when x=60 and f(x) corresponds to a value of 120. In this case, the 0/0 corresponds to a value of 120 (as "planned") and is determined by the particular function chosen.

But if if someone asks the general question "What's the value of 0/0?", the answer would have to be "Unable to be determined without further information - it could be anything." i.e. indeterminate. You can fiddle f(x) to make 0/0 correspond to any number you want (including the undefined

13. ## Re: Nothing

...and just to help Alan's visualisation.

14. ## Re: Nothing

<P ID="edit" class=small>(Edited by AlanMiller on 25-May-05 13:44. Added picture)</P>Hmmm <img src=/S/hmmn.gif border=0 alt=hmmn width=15 height=15>... I'm not sure that really helps Jezza. While it does show the discontinuity in the function, it appears that XL has decided to assign it a value of zero. I guess this makes some sense from the point of view of a computer program, which must assign some sort of value - it probably saw the numerator as zero, so assigned zero to the whole expression. In this case though, as shown, the 0/0 corresponds to a value of 120. The attached shows it more accurately I think.

Alan

15. ## Re: Nothing

Phew! Totally clear now- thanks guys.

....

...

..

<img src=/S/confused.gif border=0 alt=confused width=15 height=20> <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

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