What is the value of this term and why?

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SUMMARY

The term ej∞ refers to the expression e^(i∞), which is derived from Euler's formula e^(ix) = cos(x) + i sin(x). In this context, as x approaches infinity, neither the real part (cos(x)) nor the imaginary part (sin(x)) converges to a specific value. Therefore, e^(i∞) is concluded to have no defined value, representing a concept that leads to a circular reasoning in mathematical analysis.

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What is ej∞?
 
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salil87 said:
What is ej∞?

Well, e^(ix) = cos(x) + i sin(x). Neither of these functions converge to a point as x-->∞. So neither the real part nor the imaginary part of e^(i∞) converges to anything. So e^(i∞) has no value.
 
It's a deep, circular groove. :)
 

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