The Birthday Paradox – On Jupiter, and Beyond (2012)

Re:The Birthday Paradox – On Jupiter, and Beyond (2012) by bogomipz on Monday March 04, 2019 @10:53AM (#19302140)

I have a question. Under the section "Where did that come from?" The author states:

>"But after a bit of futzing about I found it to be remarkably close ..."

And the number under the radicand symbol he shows "ln(4)"

What is this exactly? Why is it significant?

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Re:The Birthday Paradox – On Jupiter, and Beyond (2012) by ColinWright on Monday March 04, 2019 @11:05AM (#19302246)

"ln(4)" is the natural log of 4, so it's the solution to the equation e^x=4, where e ~ 2.71828... also known as Euler's number[0].

Reading further in the post will explain where that quantity comes from, and why it's significant, but if you have any questions you can ask them via the comment box on the article.

[0] The constant "e" turns up in lots of places, you can read more about it here: https://en.wikipedia.org/wiki/E_%28mathematical_constant%29

The usual examples for how Euler's number turns up are to do with calculus and compound interest, but there are many other.

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Re:The Birthday Paradox – On Jupiter, and Beyond (2012) by bogomipz on Monday March 04, 2019 @11:17AM (#19302335)

Yes of course, thank you. I am so used to seeing the word "log" written out in things like time complexity/Big O analysis that I forgot about the natural log - ln. Cheers.

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