True or False

[lvl107]

Hi, Everyone.
Please help. I just want to know :
{1520236818720051}^2 - 166*{117993259774340}^2 = 1
True or False ?
( "^" : exponent ; "*" : multiplication )
How to test ? Thanks.

[ELSID]

False,
Just plug into a calculator

No knowledge can be certain if it is not based upon mathematics or upon some other
knowledge which is itself based upon the mathematical sciences. -- Leonardo da Vinci

[StuartBruff]

On 8/27/2009 4:15:52 PM, lvl107 wrote:
> Hi, Everyone.
>Please help. I just want to
>know :
>{1520236818720051}^2 -
>166*{117993259774340}^2 = 1
> True or False ?
>( "^" : exponent ; "*" :
>multiplication )
> How to test ? Thanks.

See my response to your previous question.
http://collab.mathsoft.com/read?127717,63

[IRstuff]

Your typical calculator would not have sufficient precision to actually show the result, were it closer.

However, in your case, the difference diverges after the 7th decimal place, so the difference is rather gigantic, and nowhere near 1.

But, the answer is VERY close to that value, around: 166.00000233659490828

Mathcad's symbolic processor uses the numeric processor as the input part, I think, so it's limited in input precision.

There are math packages that handle the precision you'd need to get the correct answer.

TTFN,
Eden

[TomGutman]

Mathcad's symbolic processor does not use the numeric processor as input and generally ignores the numeric processor. It does unlimited precision integer and rational arithmetic. But it's slow.
__________________
� � � � Tom Gutman

[IRstuff]

Well, there's some sort of limit on the inputs, then. Any more precision on 166.000002336594908278 results in zero in the M11 symbolic processor, regardless of the float setting.


TTFN,
Eden

[TomGutman]

If you use a number with a decimal point the symbolic processor does decimal floating point calculations. The default precision for symbolic floating point is 20, and if floating point calculations are invoked implicitly (by a number with a decimal point) the calculations may be done initially with the default precision, regardless of a later float keyword. This is definitely the case for MC11, it may have been fixed in later releases.

But the original request is for a calculation involving only integers, no decimal point involved, and that should be done exactly (assuming enough memory for the required number representations).
__________________
� � � � Tom Gutman

[ptc-1368288]

>...if floating point calculations are invoked implicitly (by a number with a decimal point) the calculations may be done initially with the default precision, regardless of a later float keyword. <<br> _________________________

YES ! but that is not clear as to work it out.



jmG

[ptc-1368288]

>Your typical calculator would not have sufficient precision to actually show the result, were it closer.<
______________________

I refrain mentioning "above Pentium", probably a fixed arithmetic huge machine, and asking Neil Sloane would even be more ridiculous. At least we have an idea of the result in the previous post.

jmG

[ptc-1368288]

On 8/27/2009 4:15:52 PM, lvl107 wrote:
> Hi, Everyone.
>Please help. I just want to know :
>{1520236818720051}^2 -
>166*{117993259774340}^2 = 1
> True or False ?
...
> How to test ? Thanks.
_______________________

How to test ? like this



jmG