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Dan Boschen
Dan Boschen
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Using infinity as a $point$ is really an abbreviation for a limiting process. If you draw a sequence of regions comprising an increasing portion of the $j\omega$-axis along with corresponding semicircular arcs lying in the RHP you will find using the Cauchy theorem a value for the number of zeros in each region. If there are no zeros in the RHP, each value will be zero, as is then the limit. If you were to do this with regions in the LHP, you would have different answers.

Using infinity as a $point$ is really an abbreviation for a limiting process. If you draw a sequence of regions comprising an increasing portion of the $j\omega$-axis along with corresponding semicircular arcs lying in the RHP you will find using the Cauchy theorem a value for the number of zeros in each region. If there are no zeros in the RHP, each value will be zero, as is then the limit. If you were to do this with regions in the LHP, you would have different answers.

Using infinity as a $point$ is really an abbreviation for a limiting process. If you draw a sequence of regions comprising an increasing portion of the $j\omega$-axis along with corresponding semicircular arcs lying in the RHP you will find using the Cauchy theorem a value for the number of zeros in each region. If there are no zeros in the RHP, each value will be zero, as is then the limit. If you were to do this with regions in the LHP, you would have different answers.

Using infinity as a $point$ is really an abbreviation for a limiting process. If you draw a sequence of regions comprising an increasing portion of the $j\omega$-axis along with corresponding semicircular arcs lying in the RHP you will find using the Cauchy theorem a value for the number of zeros in each region. If there are no zeros in the RHP, each value will be zero, as is then the limit. If you were to do this with regions in the LHP, you would have different answers.

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oldlab
oldlab
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Using infinity as a $point$ is really an abbreviation for a limiting process. If you draw a sequence of regions comprising an increasing portion of the $j\omega$-axis along with corresponding semicircular arcs lying in the RHP you will find using the Cauchy theorem a value for the number of zeros in each region. If there are no zeros in the RHP, each value will be zero, as is then the limit. If you were to do this with regions in the LHP, you would have different answers.