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-- e is irrational

e is irrational

If e were rational, then e = n/m for some integers m, n. So then 1/e = m/n. But the series expansion for 1/e is
1/e = 1 - 1/1! + 1/2! - 1/3! + ...

Call the first n terms of this alternating series S(n). How good is this approximation to e? Well, the error is bounded by the next term of the alternating series:
0 < | 1/e - S(n) | = | m/n - S(n)| < 1/(n+1)!

But multiplying through by n!, you will see that
0 < | integer - integer | < 1/(n+1) < 1.
But there is no integer strictly between 0 and 1, so this is a contradiction; e must be irrational.

**Insert rational e-pill joke here**

Pi > e

n00b

I finished the first sentence and wanted to shoot myself. I'm not even joking, my stress level just shot through the roof. God, I hate math.

quote:

Originally posted by idoru I finished the first sentence and wanted to shoot myself.

You too?

quote:

Originally posted by idoru I finished the first sentence and wanted to shoot you in the face. I'm not even joking, my stress level just shot through the roof. God, I hate your post.

First time I've ever done this, but...

FIXED.

ecstacy is a number?

EDIT>
e

quote:

It is known that e is irrational (proof)

i see..

Re: e is irrational

quote:

Originally posted by Pett If e were rational, then e = n/m for some integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e = 1 - 1/1! + 1/2! - 1/3! + ... Call the first n terms of this alternating series S(n). How good is this approximation to e? Well, the error is bounded by the next term of the alternating series: 0 < | 1/e - S(n) | = | m/n - S(n)| < 1/(n+1)! But multiplying through by n!, you will see that 0 < | integer - integer | < 1/(n+1) < 1. But there is no integer strictly between 0 and 1, so this is a contradiction; e must be irrational.

Of course i'm going to use the colour red as an example. It's at the end of the spectrum so the rational of clipping it doesn't require a significant leap to link the two data points into a single cohesive logical unit.

Toronto! Ya give em the CN tower and they mistake it for the Peace Tower.

fuck that. E is my friend.

E = MC^2

Two Mc's equals E. E MC's. Yo.

1+1=4?

quote:

Originally posted by Bidor 1+1=4?

not even imaginary. just wrong.

[Mr. Mackey voice]Drugs are bad, mmmkay!?! [/Mr.Mackey voice]

honestly im glad its 420, otherwise id have a headache.

i hate maths

quote:

Originally posted by Sushipunk First time I've ever done this, but... FIXED.

Right, I've seen this all over the place, WTF does FIXED mean in response to a statement?

Sorry to be thick but I've always wondered.

Jarv

quote:

Originally posted by Jarvmeister Right, First time im doing this but. Its basically when someone post something, it gets quoted and edited for either humor or correctness. Sorry to be thick but I've always wondered. Jarv

FIXED

lol

I must be even thicker than I thought. I read DrunkenMasters reply about 5 times, before I realised what he'd done!

Haha!

I now feel like one of the gang.

quote:

Originally posted by Jarvmeister I now feel like one of the gang.

You can be the token black kid. Mind if we call you Stymie?

quote:

Originally posted by Marc Summers You can be the token black kid. Mind if we call you Stymie?

Call me what you want - I just want to be included!

e is good.

MCs are gay.

and ur all going to die from aids.

lol??

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