Pretty good article here: http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/
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Colibri
General Questions Moderator
The probability of any given thread being resurrected as a zombie thread is 1/e. Except before c.
When c=Colibri.
The thread came back. Did it bring pi(e)?
e to the x dy/dx
e to the x dx
tangent, cosine, secant, sine,
3.14159,
2.71828,
come on folks lets integrate!
okay…now I just gotta ask: how to you type that ae character ?
Even the Brits have stopped writing that way in recent decades, and I thought the computer age had killed it off, along with the Encylop[ae]dia ..
What, your keyboard doesn’t have an æ key on it?
Well, OK, mine doesn’t either. On a Mac you hit option and the quote key. I don’t know for sure on PCs, but it’ll probably be Alt and a combination of numbers, if nothing else.
Alt+0230 for lowercase (æ), Alt+0198 for uppercase (Æ).
[Note: In case you haven’t done this sort of thing before, the numbers must be entered on the numpad while holding the Alt key down; upon release, the character is entered]
Alternately, Alt+145 for lowercase and Alt+146 for uppercase.
Here’s a webpage with all the extended ASCII characters you can use.
I suppose it’s 6.5 years too late, but the “mixing husbands and wives” thing above refers to derangements.
I’ve never got Alt plus numbers to work. I’m currently running Linux Mint (derived from Ubuntu), and and it just does not work.
The Alt+numbers thing is just for Windows, so far as I know.
Well here is one that hasn’t been mentioned explicitly. Suppose you are putting some money for deposit. Choose a time period, call it one period, over which the interest is 100%. For example, if it is 5% per annum, then one period is 20 years. Simple interest over one period is such that if you start with $1, you end up with $2. If you compound it once, then you end with $2.25 since at the end of a half period you will get 50 cents giving you $1.50 total and then at the end of the full period, you will get another 75 cents interest. If you compound it 4 times, you will get about $2.44. If you do it 20 times, then you get $2.65. Now what happens if you compound it every second? You might think the amount will rise indefinitely, but you would be wrong. You will have $e approximately and the approximately gets better and better as the compounding gets shorter and shorter.
That’s probably the easiest to understand property of e.
Sure it was, in post #12 by Thudlow Boink. (They used the symbols “e = the limit as n approaches infinity of (1 + 1/n)[sup]n[/sup]”, but (as they then noted) that means the exact same thing as the ubiquitous compound interest illustration, once interpreted in terms of money)
I was never able to get it to work on Windows either, but I probably wasn’t doing it correctly. Googling around, I found that on Linux, you need to press and hold <ctl> and <shift>, then type U and the 2 digit hex code corresponding to the decimal number used in Windows, then release <ctl><shift>.
So:
<ctl><shift>Ue6: æ (<alt>230 in Windows)
<ctl><shift>Uc6: Æ (<alt>198 in Windows)
I can use the regular number keys, I don’t have to use the keypad.
[/hijack]
In Linux, you can switch to the intl or dvorak-intl keymap and hold R Alt and press Z. Hold shift to make it a capital. I used dvorak-alt-intl so I had to make a small edit to the keymap file to get it to work.