       Re: Out=((5-Sqrt)/20 + (5+Sqrt)/20 ) == 1/2 ???

• To: mathgroup at smc.vnet.net
• Subject: [mg20027] Re: [mg19976] Out=((5-Sqrt)/20 + (5+Sqrt)/20 ) == 1/2 ???
• From: "Mark E. Harder" <harderm at ucs.orst.edu>
• Date: Sat, 25 Sep 1999 02:40:51 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Patrick,
Further Food For Thought:

In:=Sqrt/20 ==Sqrt[5.]/20
Out= True

Judging from your error msg. (which reproduced in my Mathematica 3.0.2, Win
NT system), Mathematica fails when it tries to evaluate Sqrt in finite
precision and make the comparison in your expression, but it will do that in
the above.  Using N[ expr, \$MachinePrecision], however, is error free:

In :=N[( (5-Sqrt)/20 + (5+Sqrt)/20 ) ,\$MachinePrecision]
Out:=0.5
In:=N[( (5-Sqrt)/20 + (5+Sqrt)/20 ) ,\$MachinePrecision]== 1/2
Out:=True

But I'm not sure just why or how it makes these decisions.
-mark

From: Patrick McLean <p_mclean at postoffice.utas.edu.au>
To: mathgroup at smc.vnet.net
Subject: [mg20027] [mg19976] Out=((5-Sqrt)/20 + (5+Sqrt)/20 ) == 1/2 ???

>Can any one explain this behaviour???
>
>hilbert% math
>Mathematica 3.0 for Solaris
> -- Terminal graphics initialized --
>
>In:=   ( (5-Sqrt)/20 + (5+Sqrt)/20 ) == 1/2
>
>\$MaxExtraPrecision::meprec:
>   \$MaxExtraPrecision = 50. reached while evaluating
>      1    5 - Sqrt   5 + Sqrt
>    -(-) + ----------- + -----------. Increasing the value of
>      2        20            20
>     \$MaxExtraPrecision may help resolve the uncertainty.
>
>        5 - Sqrt   5 + Sqrt    1
>Out= ----------- + ----------- == -
>            20            20         2
>
>In:=
>
>--
>Patrick McLean
>
>No news is good news...
>

```

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