What is the value of e^\pi - \pi?

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The claim that e^π - π equals 20 is incorrect; the actual difference is approximately 0.00021, indicating it is an "almost integer." The discussion highlights the confusion stemming from this approximation, with one participant referencing a comic that humorously presents the idea. The mathematical expression e^π = cos(iπ) - i sin(iπ) is mentioned but not fully explored. The conversation emphasizes the distinction between exact equality and approximate values in mathematics. Overall, the topic illustrates the interesting nature of "almost integers" in mathematical discussions.
rohanprabhu
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I read somewhere that e^\pi - \pi = 20.

1. Is it true?
2. I tried finding out.. but all I've reached till is:

<br /> e^{\pi} = \cos{(i \pi)} - i \sin{(i \pi)}<br />

what do i do from here on>
 
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Probably it was an engineer who told you :smile:
The difference with 20 is about 9.00021 x 10-4. So it's an approximate equality (which is, for a mathematician, of course not an equality).
 
It's a nice example of an "almost integer". Mathworld has a nice on them, its got many other expressions that are "almost integers" like yours.
 

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