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Re: Plot[(1 + 10^(-k))^(10^k), {k, 2, 9}]

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  • Subject: [mg27448] Re: [mg27427] Plot[(1 + 10^(-k))^(10^k), {k, 2, 9}]
  • From: "Christopher J. Purcell" <purcell at>
  • Date: Sun, 25 Feb 2001 20:55:53 -0500 (EST)
  • References: <>
  • Sender: owner-wri-mathgroup at

You are seeing the effect of using machine precision arithmetic.
$MachinePrecision will tell you how many digits Plot is working with 
on your computer. Instead try something like this where you can ask 
for more precision with the N function. Note I have inserted a 
missing bracket in your expression.

ListPlot[ Table[Evaluate[ N[(1+10^(-k))^(10^k),100]], 

>I happen to execute:
>Plot[(1+10^(-k)^(10^k), {k, 2, 9}]
>It looks fine if you change  {k, 2, 9} to {k, 2, 3}, but otherwise the
>plot is absurd.
>Limit[(1+10^(-k)^(10^k), k->Infinity]==E
>may I ask what's wrong with my Mathmatica 4.0 on MMX 166 ?
>Hu Zhe

Dr. Christopher J. Purcell
Defence Research Establishment Atlantic
9 Grove St., Dartmouth, NS Canada B2Y 3Z7

Tel: 902-426-3100-x389
Fax: 902-426-9654
E-mail: purcell at

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