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[wierd]

I regret being explosed to the scp website yesterday.

It consumed an entire day of my life!

(Sob)

[slothen]

Might also be worth noting at the top the premise of the entire proof is a consequence of the density of real numbers, that is, if A > B, then there must exist a C such that A > C > B.  If no such C exists then A = B.  I'm not sure exactly what this property is called.  It doesn't really need a name.  It boils down to this: if two points not the same, then there must be some daylight between them.  If two points don't have any daylight between them, then those points are the same.

0.9999.... (Q further in the text) is equal to 1 - we can prove it by proving that negation leads to contradiction.

Let's assume that Q != 1. That means a real number P must exist that falls between Q and 1, i.e. Q < P < 1 [1].

We know that P > Q. We will try to construct it's decimal representation, because any real number has a decimal representation (though transcendent real numbers have infinite non-periodic ones). The first digit must be 0 followed by decimal point - 1 and greater would mean P > 1 and -1 and smaller would mean P < Q, which would contradict the original assumption [1]. Lets find the second number.  Clearly, it must be 9 - any other value would mean that P<Q (example - 0.7 < 0.999... ). This will be our first induction step [I1].

You should have saved the "clearly" for "clearly, the first digit must be zero."  Going into detail on that confused me for awhile.

At this point I think you mixed up your P's and Q's (no pun intended).

Then we will show that for n-th (n is a natural number) digit in decimal representation of Q P, that if this number is 9, the following number must be 9 also, formally:

( d[n] = 9 ) => ( d[n+1] = 9 ) [I2]

Let's have a number S that equals 0.9999....9, and the number of nines past the decimal point is equal to n+1. Clearly, S < P Q. If our sought number Q P have anything else on n+1 th position than 9, it's clear that immediately Q P < S, and therefore P < Q, a contradiction.  and for every possible combination of the remaining digits in Q's decimal representation, Q will be always smaller than P, which is once again, contradiction, because for any digit on m-th position, where m>n, m-th digit in the representation of Q can never be higher than P's 9.  S is n+1 9's, P is n 9's.  P's n+1th digit must also be a 9 or we have a contradiction, P < S < Q.  Again our assumption is Q < P < 1.

Now we use mathematical induction using [I1] (first number after decimal point must be 9) and [I2] (the next number must be always 9 too) to prove that our sought number Q  P must be expressed only by 0.9999...., and therefore is in fact equal to P Q.

P = Q, but that contradicts P < Q < 1, that means that we have proven by contradiction that no such real number Q P that would fall between P Q and 1 exists. If no such real Q  P exists, then P Q must be equal to 1, i.e. 0.9999.... = 1

Probably didn't need to introduce S either.  Still interesting proof, haven't seen an induction-based decimal construction for this before, even though there are like a million different proofs.  I hope you don't mind my critique/edits.

[Blizzlord]

Might also be worth noting at the top the premise of the entire proof is a consequence of the density of real numbers, that is, if A > B, then there must exist a C such that A > C > B.  If no such C exists then A = B.  I'm not sure exactly what this property is called.  It doesn't really need a name.  It boils down to this: if two points not the same, then there must be some daylight between them.  If two points don't have any daylight between them, then those points are the same.

This will be helpful in math; that if there are only 2 points they are equal due to a lack of difference.

[wierd]

I always saw it this way:

1/3 = .333...
2/3 = .666...
3/3 = .999...

By definition, 3/3 = 1. Thus .999... = 1

[Blizzlord]

I always saw it this way:

1/3 = .333...
2/3 = .666...
3/3 = .999...

By definition, 3/3 = 1. Thus .999... = 1

But people lever nearn...

[wierd]

The infinitessimal is conserved without change over multiplication. This only happens when the quantity multiplied is 0.

Thus, the difference between .999... and 1 is 0.

eg, .333... * 2 = .666... 

If the infinitessimal were an actual value, it would double per the rules of multiplication. The fact that it doesn't, shows that the value for the infinitessimal is 0.


Algebraically, to provide a value for the infinitessimal:

(.333... + X) * 3 = (.999... + 3X)

For X = 3X to be true, X == 0.

[KodKod]

While "on" the topic, is there anything anybody else wants to regret doing.

I regret not watching ponies recently.

I regret that every time I spend hours labouring over a carefully planned scheme the execution always either fails completely or lacks flair.

[wierd]

Silly girl Kodkod,

The reason is simple!  You keep making *<*PLANS*>*, when what you need to make are !!*<*PLANS*>*!!

How do you expeect there to be "flair" without the !!<>!!?

[KodKod]

Who said anything about "plans"? No, no. I scheme, I plot, I contrive.
Give me credit where sinister credit is due.

[wierd]

I'm a sadistic schemer myself!

Here's my angle:  the punishment must fit the crime.  The more ironic the sadistic punishment compared to the crime, the more beautiful it is.

Take for instance, my 12th birthday.  My cousins from Alabama had come to visit. My cousin and I have birthdays a single day apart. Because of that, we had a combined birthday party.  While setting everything up, we discovered we didn't have icecream, so we all packed up and headed into town to get some.

While we were gone, the neighbor kid, whom I DID NOT invite, snuck into my house, stood on a shelf inside the cabinet that was filled with mason jars filled with mom's home-made spaghetti sauce, and literally gorged his fat little face with his grubbly little hands with my and my cousin's birthday cake, ruining the cake, breaking the shelf in the cabinet, breaking the jars of sauce all over the kitchen floor.

This is when I started creating the !!*<*EVIL PLAN*>*!!.

This kid could not resist sweets in any form. At the time, I was a consumate creator of sweet, delicious confections. (Baking is a vice, I swear. There is nothing as dangerous as knowing how to make delicious cake whenever you want.) Using this terrible knowledge, I concocted a new form of evil.

Habenero chocolate fudge brownies.

I created them using a small pressure cooker, slightly ground habenero pepper seeds, a few table spoons of everclear (refined corn alcohol. 99.7% ethanol), and about a cup of water.  Using the pressure cooker and the edible solvent solution, I extracted the capsacin from the habenero seeds, strained the mix through a coffee filter, and used the resulting liquid fire to create half of the brownie batch.  The other half used milk instead.

In terms of texture, flavor, and color, the only difference was that the habenero ones were slightly darker, and had a delayed onset of "pepperspray intense" hotness.

Armed with my deadly confections, I went past the party pooper's house, to his *other* neighbor. I told that neighbor kid all about what happened, and my viscious evil plan.

You see, his house had a side door that directly faced the party crashers.  Sitting on that porch with a pitcher of milk, we ate every last one of the "safe" brownies, in direct sight of the offender. The offending little oinker asked repeatedly if he could have a brownie.  We told him no, he could not.

After eating all the good brownies, we acted full, and retired to his back yard behind the privacy fence to jump on the trampoline; leaving the platter of evil ones right there on the porch unprotected.

About 5 minutes pass, and then we hear an awful, blood curdling shriek, followed by unimaginable wailing, and a door slam.

The slam was not the door of the offender's house.

Worried that I had dosed the younger baby brother of the kid I had recruited in my evil plan, I rush inside to find not an innocent youngster, but the intended mark, blubbering, shreiking, and trying to wash his eyes in the sink with warm water......

The idea that he would rub his eyes with hot pepper juiced hands, essentially pepperspraying himself, had not occured to me.  However, the result was absolutely delicious.  Being the big softy that I am deep down inside, I pulled him away from the sink, stuffed him into a kitchen chair, and saturated a fresh paper towel with cold milk and told him to use it like a compress. 

Needless to say, his mother was exceedingly cross with me. I bluntly told her that I didn't offer him any, and that he shouldn't have taken them.  (She didn't like that too much.)

Inspection of the plate revealed that he managed to inhale 5 brownies before the 2-3 second delay kicked in.

Let's just say he never dared to eat any of my desserts ever again.

[Kogut]

I am not sure how this is relevant to thread and whatever this happened (ah, joy of the internet) but this story is awesome!

[KodKod]

Hmm... subtle and clever, I like it. Though considering what the little bastard did to you I’m surprised that you weren’t any harsher than that.

Still, it sounds like you got the message across, which is excellent. Some people never learn that their actions have consequences. Fine storytelling.

I’ve never extensively considered delivering poison via delicious treats before, though that may have something to do with the fact that I wouldn’t want to poison anyone who would actually accept cake from me and not find it the least bit suspicious.

[wierd]

That was the most delicious part!

I told him he COULDN'T have any.  Every kid knows that being denied the candy makes you crave it all the more.  Simply giving him the evil brownies would not have punished the crime, which was stealing food and then lying about it.  No no, he had to bring the pain upon himself through his choice to engage in vice.

This is why I was worried about accidentally hitting the baby brother... punishing somebody that did not do the crime and isn't really old enough to know better (a 3 year old) was simply unacceptable, even to me.

Part of the background behind the story was that my victim had become a little too comfortable sneaking into other people's houses to raid their refrigerators.  The kid I recruited had experienced several such home invasions, due to the quick and convenient access via that side door. As such, he was very easy to recruit for my cause. Hilariously, his folks supported my "he shouldn't have taken them" position against the victim's mother.

My own mom however, was greatly displeased, and grounded me for my "unchristian" behavior. I accepted the punishment with dignity.  It was worth it.

[KodKod]

Ah, there is no pleasure greater in this world, no more powerful high, than the thrill of an unabashed, delectable vengeance against those who have done you wrong; the sickly sweet symphony of despair from a victim who knows full well that they brought it upon themselves moves me in ways that no great work of art could ever hope to compete with.

Still, there comes a time in everyone’s life where “Hey, don’t eat this cake which is definitely not poisoned or anything” simply won’t cut it anymore. But that just means more props to you for taking advantage of a situation in which it worked out, and so young!

And shame on your mother for punishing you at the time. Parents are supposed to encourage creativity in their children.
 

"I don't know who the Night Mother is, but she pays me to kill people. My own mother should have loved me so much."

[Loud Whispers]

The plan was flawed, but I like it. Probably needed more laxatives.