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Author Topic: Your life story in six words.  (Read 161279 times)

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Offline Izzy1337

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Re: Your life story in six words.
« Reply #2450 on: October 03, 2011, 02:35:13 PM »
Izzy was recently accused of vampirism...

Offline Mordred

Re: Your life story in six words.
« Reply #2451 on: October 03, 2011, 10:26:15 PM »
Today, braindead took on new meaning.

Offline Zaer Darkwail

Re: Your life story in six words.
« Reply #2452 on: October 04, 2011, 02:31:26 AM »
Too much school paperwork single week

Offline Qt

Re: Your life story in six words.
« Reply #2453 on: October 04, 2011, 03:24:31 AM »
I is mad, uni kill me

Offline Izzy1337

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Re: Your life story in six words.
« Reply #2454 on: October 04, 2011, 12:43:40 PM »
Sometimes, murder should be more legal...

Offline Twilightfiredragon

Re: Your life story in six words.
« Reply #2455 on: October 04, 2011, 01:07:12 PM »
Ex-racer missing his favourite fast car.

Offline Jaq

Re: Your life story in six words.
« Reply #2456 on: October 04, 2011, 05:36:51 PM »
Thwarted supervillain returns to strike again.

Offline InariShiftskin

Re: Your life story in six words.
« Reply #2457 on: October 04, 2011, 06:21:13 PM »
A mindless slog through empty hours.

Offline Mordred

Re: Your life story in six words.
« Reply #2458 on: October 04, 2011, 06:27:22 PM »
Scrambling to return to level zero.

Offline Twilightfiredragon

Re: Your life story in six words.
« Reply #2459 on: October 04, 2011, 07:05:22 PM »
tired as hell need more coffeee

Offline Mordred

Re: Your life story in six words.
« Reply #2460 on: October 04, 2011, 07:15:31 PM »
Contemplating leap from -1 to +1.

*as the wind causes the rickety stairway to sway with creaks and groans.. hehehe.. and that gorgeously wicked shadow below licks it's insatiable chops as it waits for this mad vampire to fall.. and the mad vampire wonders where his lovely pool of blue jell-o is now, eh? :P*

Offline Mordred

Re: Your life story in six words.
« Reply #2461 on: October 05, 2011, 03:03:12 PM »
Feelings shadow's full power once again. :D

Offline WhiteTigerForever

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Re: Your life story in six words.
« Reply #2462 on: October 05, 2011, 03:07:07 PM »
Contemplating leap from -1 to +1.

*as the wind causes the rickety stairway to sway with creaks and groans.. hehehe.. and that gorgeously wicked shadow below licks it's insatiable chops as it waits for this mad vampire to fall.. and the mad vampire wonders where his lovely pool of blue jell-o is now, eh? :P*

oh noooooz you didn't...take this!!! XD


1 is not actually defined to be greater than zero, it can be proven. The real numbers are an ordered field (technically, a complete ordered field, but completeness is not needed in this proof). If you are unfamiliar with the field axioms and the definition of a total ordering, you should look those up first. In fact, since there are different ways of defining a total ordering, I'll just give you the definition I'll be using:

If S is a set, define a subset P (called the positive set) by the following three conditions:

1.) Elements of P are closed under addition
2.) Elements of P are closed under multiplication
3.) If x is an element of S, then one and only one of the following are true: a is in P, -a is in P, a = 0

The third condition is called the law of trichotomy. -a is defined to be the additive inverse of a and 0 is defined to be the additive identity. We define the order relation > by

a > b if and only if a - b is an element of P.

Now, before proving this, I have to start with a lemma. I need to prove that if a is a non-zero real number, then a^2 > 0 (meaning it's in the positive set).

Suppose a is a non-zero real number. By the law of trichotomy, either a > 0 or a < 0. If a > 0, then by closure of multiplication in the positive set, a^2 > 0. If a < 0, then -a > 0. So,

a^2 = aa = (-a)(-a) = (-a)^2, which is in the positive set, again by closure. Thus, a^2 > 0 in all cases where a is not equal to zero.

Note that I didn't justify the step aa = (-a)(-a). This can be proven as well, but this is taking long enough as it is, so I'll let you figure it out (it's not that hard if you use the distributivity axiom). Now, onto the proof.

We first want to show that 1 is not equal to zero (bear in mind that 1 is defined to be the multiplicative identity). We'll do this by assuming the opposite and arriving at a contradiction. Suppose that 1 = 0. If a is a non-zero real number, we have a = a*1 = a*0 = 0, which is a contradiction (because we assumed a was non-zero). Note that the step a*0 = 0 was also unjustified. Again, this isn't difficult to prove using the field axioms, but I'd rather not get any more off track.

So, since 1 is not equal to zero, then the law of trichotomy says that either 1 > 0 or 1 < 0. Now, by the definition of multiplicative identity, 1^2 = 1*1 = 1. However, our lemma says that given any non-zero real number a, a^2 > 0. Thus, 1 > 0.    hee hee hee ;D

Offline Izzy1337

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Re: Your life story in six words.
« Reply #2463 on: October 05, 2011, 03:41:03 PM »
Can you translate that from Math?

Offline WhiteTigerForever

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Re: Your life story in six words.
« Reply #2464 on: October 05, 2011, 03:50:18 PM »
*giggles* You made me smile big! :D

Offline Izzy1337

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Re: Your life story in six words.
« Reply #2465 on: October 05, 2011, 03:56:59 PM »
Thanks, glad I can help someone.

Offline Mordred

Re: Your life story in six words.
« Reply #2466 on: October 05, 2011, 04:09:46 PM »
*Simply plans on spreading unlimited chaos* :P

Offline WhiteTigerForever

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Re: Your life story in six words.
« Reply #2467 on: October 05, 2011, 06:10:32 PM »
ooooohhhhh dearest Mordred... we could have great fun discussiog "chaos"  XD  ;D or 0Kelvin..XD

Offline Ephemera

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Re: Your life story in six words.
« Reply #2468 on: October 06, 2011, 05:59:09 PM »
I love more than just one.

Offline WhiteTigerForever

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Re: Your life story in six words.
« Reply #2469 on: October 06, 2011, 10:45:16 PM »
Wrote things in the wrong place.

« Last Edit: October 06, 2011, 11:33:29 PM by WhiteTigerForever »

Offline Ephemera

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Re: Your life story in six words.
« Reply #2470 on: October 06, 2011, 11:43:04 PM »
only six is not enough for...

Offline Izzy1337

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Re: Your life story in six words.
« Reply #2471 on: October 07, 2011, 10:25:07 AM »
...Anything that's of use to anyone.

Offline Mordred

Re: Your life story in six words.
« Reply #2472 on: October 07, 2011, 11:33:44 AM »
Desperately trying to clear brain fog. :(

Offline Izzy1337

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Re: Your life story in six words.
« Reply #2473 on: October 07, 2011, 11:37:48 AM »
Good luck with that, Mr. Blue.

Offline Mordred

Re: Your life story in six words.
« Reply #2474 on: October 07, 2011, 12:27:45 PM »
Time to re-embrace the elusive shadow.