Disproving Euler's Identity: Check My Math

  • Thread starter Onyxus
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In summary: But I will definitely take the time to read up on the complex logarithmic function.In summary, the student was experimenting with Euler's Identity and believes they may have disproved it accidentally. They are seeking assistance in checking their math to ensure they did not make any beginner mistakes. However, it is pointed out that the error may lie in their understanding of complex numbers and the definition of the logarithmic function.
  • #1
Onyxus
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I was messing around with Euler’s Identity and I think I accidently disproved it. I would like someone to check my math to make sure I didn’t make any rookie mistakes.

[tex]
\begin{array}{l}
e^{\pi i} + 1 = 0 \\
e^{\pi i} = - 1 \\
\left( {e^{\pi i} } \right)^2 = \left( { - 1} \right)^2 \\
e^{2\pi i} = 1 \\
\ln \left( {e^{2\pi i} } \right) = \ln \left( 1 \right) \\
2\pi i = 0 \\
\frac{{2\pi i}}{{\pi i}} = \frac{0}{{\pi i}} \\
2 = 0 \\
\end{array}
[/tex]
 
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  • #2
So, how did you define the logarithm on complex numbers??
 
  • #3
ln(1) = 2kπi, where k is any integer. ln is a multivalued function.
 
  • #4
Onyxus said:
I was messing around with Euler’s Identity and I think I accidently disproved it. I would like someone to check my math to make sure I didn’t make any rookie mistakes.

[tex]
\begin{array}{l}
e^{\pi i} + 1 = 0 \\
e^{\pi i} = - 1 \\
\left( {e^{\pi i} } \right)^2 = \left( { - 1} \right)^2 \\
e^{2\pi i} = 1 \\
\ln \left( {e^{2\pi i} } \right) = \ln \left( 1 \right) \\
2\pi i = 0 \\
\frac{{2\pi i}}{{\pi i}} = \frac{0}{{\pi i}} \\
2 = 0 \\
\end{array}
[/tex]



What gives you away as a rookie is the title of your post, not your mathematics...which are also wrong.

Perhaps you'll be interested in reading about the complex logarithmic function's definition...

DonAntonio
 
  • #5
edit: student posted under my account
 
  • #6
Thank you, DonAntonio, mathman and micromass, I thought that was what my error was, but I wasn't sure. You see, I haven't yet taken a course in which I learn even the basics of complex numbers, so my knowledge in that area is rather lacking.
 

FAQ: Disproving Euler's Identity: Check My Math

What is Euler's Identity?

Euler's Identity is a mathematical equation that connects five fundamental mathematical constants: 1, 0, pi, e, and i. It is written as e^(i*pi) + 1 = 0 and is considered one of the most beautiful equations in mathematics.

Why do people want to disprove Euler's Identity?

There is a common misconception that disproving Euler's Identity would somehow discredit or undermine the field of mathematics. However, mathematical concepts and theories are constantly being challenged and revised in order to further our understanding of the world around us. Thus, disproving Euler's Identity could potentially lead to new discoveries and advancements in mathematics.

What is the current consensus on Euler's Identity?

The vast majority of mathematicians and scientists accept Euler's Identity as a true and valid equation. It has been extensively studied and has been proven to hold true in various mathematical contexts. However, there are still ongoing debates and discussions about its implications and applications.

How can one go about disproving Euler's Identity?

In order to disprove Euler's Identity, one would need to find a counterexample or mathematical proof that shows it to be false. This would involve extensively studying and analyzing the equation using various mathematical tools and techniques. It is a challenging task that would require a deep understanding of mathematical concepts and theories.

What would be the implications of disproving Euler's Identity?

If Euler's Identity were to be disproven, it would have significant implications for mathematics and potentially other fields such as physics and engineering. It could lead to a shift in our understanding of fundamental mathematical concepts and could open up new areas of research and exploration.

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