The way you think about the exponential function is (probably) wrong. Don't think so? I'll convince you. Did you realize that multiplying e by itself π times doesn't make sense? Here is what's really behind the most important function of all time.
This is great but I came here after clicking an article on LinkedIn which talked about exp(pi). There is no mention of that in this article, e.g. why it is so important.
Thanks! It was just an example to illustrate that thinking about exponentiation as repeated multiplication is quite absurd if we go beyond positive integer exponents.
This is great but I came here after clicking an article on LinkedIn which talked about exp(pi). There is no mention of that in this article, e.g. why it is so important.
Thanks! It was just an example to illustrate that thinking about exponentiation as repeated multiplication is quite absurd if we go beyond positive integer exponents.
Nice Explanation. We can define a^x as e^{x ln a}.
Is this absurdity also seen in application of exponentiation to solve real problems in nature ?
I am wondering if this is an aspect of nature.
This is bordering philosophy, and I am not good in that :)
I render the formulas with QuickLaTeX (https://quicklatex.com/), and put the images together in Inkscape.