Re: Demonstrate that 1==-1

• To: mathgroup at smc.vnet.net
• Subject: [mg23197] Re: [mg23171] Demonstrate that 1==-1
• From: Daniel Lichtblau <danl at dragonfly.wolfram.com>
• Date: Mon, 24 Apr 2000 01:12:05 -0400 (EDT)
• References: <200004210348.XAA19777@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Alberto Verga wrote:
>
> Compute
> Integrate[(1 + a/E^(I*u))/(-1 + a/E^(I*u)), {u, 0, 2*Pi}]
>
> Mathematica gives -2Pi
>
> Now multiply the numerator and the denominator by -1
>
> Integrate[(-1 - a/E^(I*u))/(1 - a/E^(I*u)), {u, 0, 2*Pi}]
>
> Mathematica gets 2*Pi
>
> This is only possible if 1==-1
>
> Is this another bug in Limit?
>
> Alberto Verga
> irphe - Marseille

No, it is a bug in Integrate. To see this, try:

Unprotect[Limit];
Limit[a:___] := Null /; (Print[{a}]; False)
Integrate[(-1 - a/E^(I*u))/(1 - a/E^(I*u)), {u, 0, 2*Pi}]
Integrate[(1 + a/E^(I*u))/(-1 + a/E^(I*u)), {u, 0, 2*Pi}]

You will find that Limit is never called.

I will look into the Integrate problem.

Daniel Lichtblau
Wolfram Research

```

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