Official thread of math awesomeness (official)

[Cheebs]

Math can really turn my crank. This thread is for like-minded nerds and curiosity-seekers.

While looking through some of my old texts I was reminded of this neat little tidbit: 0.999... where the 9's keep repeating forever is equal to 1. Not just really, really close to 1, but literally equal to 1. The proof:

a = 0.999...

10a = 9.999...
now subtract "a" from each side

9a = 9.999... - 0.999...
9a = 9
a=1

Rock on.

A simpler example:
1/3 = 0.333...
2/3 = 0.666...

so obviously 3/3 = 0.999...
but also obviously 3/3 = 1

I love simple proofs with non-obvious results.


Another favorite of mine is the "Monty Hall" paradox. Not really a paradox, but a great one for the statisticians to chew over. It goes like this: You are on Monty Hall's game show. There are three doors. Two doors have a goat, one door has a car. Monty Hall knows where the car is.

You get to choose a door. After you choose, regardless of your choice, Monty Hall opens up a goat door while keeping your door closed. He then gives you the option to switch your choice from your initial pick to the other remaining door.

The question is: Is there a statistical advantage to switching doors at that point in time?

The answer is: Yes, if you switch every single time you will win the car 2/3 of the time. People will argue 'til they're blue that when presented with the two remaining doors it's a 50/50 chance so it doesn't matter, but run a simulation yourself with three playing cards and the 2/3 victory margin will quickly become apparent.

The really spiffy thing: If Monty hall doesn't know the location of the goats beforehand your chances stay at 50/50.

Wikipedia lays it all out here.


So, discuss, post math awesomeness of your own, or just type "lol gay".

[cka]

nerds itt

to contribute, uhh... variable & 1 is loads faster than ((variable % 2) == 0) in programming for doing things like checking if an element in a huge array is even or odd-numbered

here's a nice write-up on it

[Timber]

I <3 math

[YellerDog]

Math it up!

RHOMBUS

[kingoffighters]

There is another statistical paradox.

You flip a coin, if you guess right, then you double your money. If you don't, you lose everything. What would your expected winnings to be (say you do this a billion times)?

[mannerbot]

So Cheebs has never taken calculus?

[Cheebs]

So Cheebs has never taken calculus?

Mr Cheebs has a mechanical engineering degree.

[Cheebs]

There is another statistical paradox.

You flip a coin, if you guess right, then you double your money. If you don't, you lose everything. What would your expected winnings to be (say you do this a billion times)?

I would say your winnings would be zero. After 3 flips if you're really lucky.

[kingoffighters]

I would say your winnings would be zero. After 3 flips if you're really lucky.

The expected value is infinite.

[burgundy]

.999... < 1