Euler's 'e', is, the unique number for which the derivative of the exponential function 'e to the x' is itself 'e to the x'. It is also known as the root of the natural logarithm (the inverse of the exponential function). As my professor once responded when he was asked if he was talking about the natural logarithm; "There is only one logarithm". All other logarithms, such as the common log10 function, are defined in terms of e and the natural log. The exponential function and the natural logarithm illuminated negative exponents, non-integral exponents, and imaginary numbers, without which we would live in a very different world, although we would certainly still have ample opportunity to keel over from a stroke, with or without grandchildren, orange slices, or any inkling of the numerous possible connections between them.
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Oooh, just like "The Godfather". Did he have an orange slice in his mouth?
Euler's 'e', is, the unique number for which the derivative of the exponential function 'e to the x' is itself 'e to the x'. It is also known as the root of the natural logarithm (the inverse of the exponential function). As my professor once responded when he was asked if he was talking about the natural logarithm; "There is only one logarithm". All other logarithms, such as the common log10 function, are defined in terms of e and the natural log. The exponential function and the natural logarithm illuminated negative exponents, non-integral exponents, and imaginary numbers, without which we would live in a very different world, although we would certainly still have ample opportunity to keel over from a stroke, with or without grandchildren, orange slices, or any inkling of the numerous possible connections between them.
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