Axiom of Choice

Is it true?

Then prove it.

1) Yes

2) Simple consequence of zorn's lemma, or the well ordering principle.

>>1
You don't know what an axiom is, huh?

>>3
They just called it that because it's a theorem they couldn't prove.

>>4
What? Choice? Please. I got that shit down pat!
Choice is binary, To do or not to do (in regards to options).
Options are variable, to open a door or to NOT open a door; to pull or not to pull, to push or not to push.
Of course this is just an analysis of something that is naturally occurring in all things...whether the source of the choice is aware of it or not is wholly beside the point. We being human can discern choice entirely because OF our awareness. Of course, you would actually have to be looking for it to find it. It's something so subtle and small that it is most commonly overlooked.
"It is the small things that matter."
"It is often times the simplest things in life that are most commonly overlooked."
"I tell you to look at something in a certain direction and when you turn to face it you say it doesn't exist; I say open your eyes first." Somethings are just not easily understood especially if they aren't looked at. If I tell you to see this amazing thing at the beach, will you know what I'm talking about? You would go around seeing all these neat and wonderful things; most likely, you won't even pass a glance at what I was actually referring to. How can I tell you that you are reading this line? How can I tell you that you are having an emotional reaction now? How can I tell you that you are trying to figure out my intention now? How can I tell you that you are trying to shake me off like a bad hangover now? Not all things are easily explained, understood, or grasped. The point is to continue looking UNTIL an explanation comes, until it is understood, until it is grasped.
"It's not a matter of how far you are willing to take it; it's a matter of how willing you are to take it as far as it needs to go."
The only purpose for choice is motion or stillness. The only need of stillness is to remain. The only need of motion is to be. "To be or not to be." This is why atoms as a wave-form can appear as particles. They wish to be seen. They wish to matter and so they become matter.
Axiom; a generally accepted truth without the need for proof.

The issue we are faced with between things such as choice, free-will, honesty, integrity, honor, bravery, courage and action is the issue between intangible and tangible things.
If you were told to prove the existence of something intangible, how might you go about proving it? Einstein proved the existence of atoms by what was NOT present. When those pollen were placed into water, the pollen moved. This indicated that something was pushing them around. By the distance that the pollen were displaced, that is the amount of motion of the atom.
In order to prove the existence of something that you think you know exists, first try proving it by what ISN'T there. And then, if that yields no results, try using what IS there. What you are looking for is what IS happening...not what ISN'T. What isn't happening is everything but what is; get it? So saying something that isn't happening by observing what is, is cookie-cutting the present moment observation, excluding what IS happening.

>>4
It's been proven (by Godel and Cohen) that it cannot be proven or disproven from the other axioms of ZF.

>>5
Oh look, AnONyMous2U is back, with a new name (as if he needs to name his posts).

>>6
yeah, that's because it's the same issue as with trying to prove the existence of atoms without a powerful microscope.
Choice exists, otherwise, we wouldn't be moving at all. :3
Choice coincides with motion, stillness, and allowance.
Whatever allows motion or stillness is a result of choice.
Whatever moves is doing so as a result of choice.
Whatever is still is doing so as a result of choice.
Choice precedes action, but cannot be utilized prior to reaction.

ie. you may see (choice=past, action=present, reaction=future)
however; (action=past, reaction=present, choice=future)
utilizing the latter will allow you the ability of free-will; the prior enslaves you to external force.
The reason for this has to do with the differences between what IS and what IS TO BE. What we are as intangible spirits in a very tangible body is the promotion of WHAT IS TO BE, the reaction of this is what we are privy to; the present. Therefore, the action that caused the effects we are seeing (in the present) are formed in the past. The past we can't change. This we know implicitly. The future we can change. This we know implicitly. The present is what we observe. This we too know implicitly.
The process of WHAT IS is not the same as WHAT IS TO BE. The difference is timing. The perceiving individual has one timing based upon observation of reaction (present). The one choosing to act whereby a reaction occurs is observing his thoughts at present and viewing the observers reactions at present. However, through empathy (the ability to see from another point of view) allows for us to see someone else not being able to see another person's choice because it happened in THEIR own past not the observers. However, each choice, as a generalized observation, is occurring continually in the future.
As long as it does, choice can be changed.
As long as choice remains in the past, it cannot be changed.
The rest is for you to decide for yourself, to discover for yourself, to integrate or forget. That choice is yours, I understand this because you haven't made that choice until the possibility is made by me clicking reply, and you reading this final line of text. Good luck!

Ah, and to clear up some further confusions; >>8 has implications when involving source and destination.
If an observer is viewing (at present) a motion (reaction at present) as the source; the choice would be the destination, the amount of applied motion to induce change by the observer, and Free-will to apply that motion thereby inducing change by the observer onto the observed.

The way that this works has to do with the differences in time. Time is offset and not absolute throughout everything. You might be able to view perceivable motion as time, but the intervals of perception are variable depending upon variable brain activity and directed awareness and attention. The motions outside the human perceiving is different from all that is outside of the human perceiving therefore time is offset as such. You can't change a person's choice because to you, it's already happened evidenced by reactions of the present, therefore their past you cannot change. You can change their future, their choice, by choosing to restrict or arrest another person's choice; WARNING: this application will induce a physical reaction of resistance to applied force.
Once your choice is made, the other person cannot change your choice, because to them it is in their past, evidenced by your observable reaction by them at present. All they can do is attempt to restrict or arrest your choice in the future by acting (thoughts taking place now about future events). When this is complete, you will evoke the same responses of resistance to restriction or arrest. No human alive wishes to have their motions restricted or arrested. The awareness of this causes depression, anxiety, fear, and eventually if left unchecked; suicide.
You see. The choice of suicide was something foreseen by depression, foreseeable even further back by a person's own awareness that their choices may be restricted or arrested. It is the awareness of this that creates the choice in the future. Suicide therefore becomes inevitable; unless, as an exception, that choice is interrupted. For every action there is an equal and opposite reaction. The use of all of these very human abilities is called Integration. The human trait itself is known as Integrity. When all things human are connected and move as one; that is Integrity. A lack of integrity is a segregation between human parts known and unknown. In order to account for ALL things, one must include X.
X = unknown factor of influence. Ignoring this, just because we don't know it exists due to lack of experience, and/or observation is the entire field of Religion. To view all things, you must include the unknown. Ignoring this is feigning ignorance. Especially now that you are aware of the possibility.
X may include but is not limited to a simple reaction or multiple reactions causing influence. That is the whole in the truth of everything. "Always seeking." "Knowing that we cannot know everything." These two ideals focus on one implicit truth. "Not everything known is real; not everything real is known."
If it is in your mind, it is illusion to others. It remains as illusion until YOU bring it out of your mind and into other people's reality. At this juncture, your produced illusion becomes reality to you as something tangible, to them as possibility for themselves. An illusion is not a possibility for others. An illusion is only a possibility for you. All minds are filled with possibilities which others will perceive as illusion because those same possibilities do not exist within their own minds. Knowing this, and that there is an X factor involved, means we exist and so does God. God is the X factor. Seek God and you seek your own self.

Da svidaniya.

>>7
Does that you recognize me by my vernacular? Are you crushing on me, >>7?

>>10
Does that you recognize me by my vernacular?
I accidentally the English language

>>11
ohhhhh. Good catch!
Would you like to be my proofreader from now on? I can't pay you anything, but since you've proven to me that you're willing to do things for free; I'll take you on at no extra charge. How does that sound?

Isn't it funny that after I get done posting, nobody attempts to argue back much...always with the one-liners. I must be making an impression; I'll keep up the good work, then, eh? :3

Axioms are building blocks we choose to base the rest of our mathematics upon, you can't prove it without some more basic axioms. /thread

Wait a minute...proving an axiom with another axiom is a veritable house of cards? Unless it can be replicable or observable through experiment, isn't it just pure folly?

And isn't most religions just forms of axioms?
Might even speculate that the differences between science and religion is inductive and deductive reasoning? Both are logical processes, but science doesn't want to be wrong from the start so they don't make no assumptions as a form of relative momentary truth, they just want to be ignorantly poking and prodding and becoming intellectually sound. Honestly, it sounds like two different roads to becoming an intellectual. One takes the high road, one takes the low road; both lead to a destiny, death. There, problem solved.

It does not matter wether or not the axiom of choice is true. It is an axiom and therefore considered to be true.

Is it true that after every integer comes another integer?

Pf: Let n be an elt of Z.  One can then add unity to n, giving n+1.  By definition, n+1 is an elt of Z.

(My reasoning is flawless and omits nothing of relevance!)

You can prove with this,
Or you can prove with that,
You can prove with this,
Or you can prove with that,
You can prove with this,
Or you can prove with that,
Or you can prove with us

>>15

Pure maths is not based on verifiability. If you had axioms which implied the axiom of choice, it would not be an axiom, it would be a theorem.

You simply choose axioms and deduce everything you can with them, ZFC is good to work with because it implies everything (well almost everything) we consider to be desired in mathematics.

You can choose batshit insane axioms, it will still be a valid mathematical system, just most likely not compatible with the real world or our modern mathematics today.

>>pure maths is not based on verifiability.
>>pure maths...verifiability.
>>pure verifiability.

Thanks for sharing your incompetence.
I'm sure we're thoroughly infucted with cock-in-eye disorder.

>>21

[] funny
[] to the point
[] interesting
[] uses the [x] system
[x] faggotry

>>22
Thank you for sharing a part of yourself with us, we are thoroughly bored now. :3

>>22

[x] Butthurt

[x] Responding to retard

>>24
and this is me responding to retard, now we are even. :3

>>24
[x] Butthurt
Back to the imageboards, please.

>>26
make me. :3

It is said scientifically,
"One sure test to prove Self-Awareness is to place a sticker on a child's face and place the child in front of a mirror. When the child sees the image in the mirror it will recognize the sticker and instead of reaching towards the mirror, the child touches the sticker on their own face. For the image in the mirror and the self are one in the same."

"Now we see only an indistinct image in a mirror, but then we will be face to face. Now what I know is incomplete, but then I will know fully, even as I have been fully known." -1 Corinthians 13:12; International Standard Bible.

To know of our destination of what we wish to achieve is to know where we are not.
To know we are not yet at our destination is to know we are presently somewhere else.
To realize that which we are not is to know our source.
To know our source is to know ourselves.
To be separate from our destination is loneliness.
To (re)unite with our destination is to be wholly ourselves.
And to see all God as a living being is to see ourselves as a living being. For not only are we a living being...but that we KNOW we are, and from this live accordingly.
To know that we know is the essence of being grateful.

"The scariest thing in the world isn't precisely the unknown, the scariest thing in the world is not knowing ...ourselves. Without this knowing, how may we appreciate what we have?"

Build upon your successes; learn from the mistakes of others.
When integrity includes solidarity, diligence, integration, and unification; the parts will have become whole acting as one. That it is read...so that it may be chosen.
TO DO or NOT TO DO.

"To be or not to be, that is the question."
~William Shakespeare

tl;dr "For now we know that we cannot know, but because we know this, we know...and are silent."
-Baphomet; Akron/H.R. Giger Audio CD & Tarot set

Do you not mean fail to disprove?

If I were a solipsist, I would agree with you. Seeings that I believe that you can exist outside of myself, and that I can't know everything...I would say that the Axiom of choice is valid until proven otherwise.

So...prove the non-existence of something intangible and I will be the first to congratulate you for having learned everything in existence...perhaps then, we would call YOU God seeings how you would be "All-Knowing."

My basic philosophy that works EVERY TIME is, "It works until you've proven it doesn't."

Anything else is 100% pure laziness, or perhaps I should say cowardice seeings that there is a fear about learning something because it means you didn't know it before which also means you were once ignorant...Oh...wait...you don't want to be seen as ignorant, amirite?

It's funny how fear and pain seem like such bullies to people, to me, they are my prey. I hunt them out to devour them from myself for they may only be affected within me from my own humble perception. Without the axiom of choice, it means I would have to live with what I am forever...that's ludicrous.
I am a man, always changing, always adapting, always learning, always growing. Even now as you are reading this...the same is happening to you...though you may not be aware or even thinking about this process...it is happening. And because change occurs outside of our minds means that our minds must adapt to what is changed or it degrades back from whence it came into illusion.

Sorry. It's the painful truth that you don't want to face...and that's why you are on here like me, trying to keep from doing something painful or fearful...for me, I dread going to sleep.
Every day I wake up and feel like I have just been born, stretching, getting used to temperature changes, light affecting my eyes, muscles in near-atrophy, etc. Yeah, sleep, I don't like it, but it is necessary at this stage in evolution. I guess it has something to do with metabolism and is linked through our eyes and our reptilian-portion-brain. This is why we rub our eyes when we are tired and why we have trouble staying awake after long days also.

Yeah....autodidacticism...it is a bitch...but it beats false belief any day. Sorry, I don't advocate remaining ignorant or promoting ignorance nor feigning ignorance or worse feigning intelligence. I share what I know from my own research. I've been busy for the last two years! :3

Too afraid, good, means that path IS the right direction.
Too painful, good, means that way IS the right process.

Of course, you would also have to learn to differentiate between things instead of seeing things as comparable. Stop using metaphors, similes, synonyms to describe a thing...get the REAL word and USE the real word.

Of course, with people it's different, you actually have to learn THEIR "internal dictionary" and use THEIR words with them so that THEY understand.

Of course, that means interacting with other people and learning something when supposedly everything's already been done and there is no point in exploring anything anymore cause it has already been explored...supposedly. I just have one question...was it YOU that did all those things? Was it YOU that did the exploring? Then possibly what you know isn't from Your experience, but someone else's. Don't you know, that still counts as imagination? Lack of experience + knowledge = imagination. Experience + knowledge = wisdom. :3

Sorry. Truth hurts...heal, move on, make money, screw bitches, make brats, and die...Sucks to know that up front, sucks worse to do it, is fun when the results come in...you will find something that you never new you loved just with a little experience under your belt.
"When you feel like doing anything else, that's what makes this moment the most important. Do what you don't feel like doing."

See what IS (logic)"that you are reading this at this moment in time.", what is wrong is what is right (innocence)"Slut? That's funny. I thought that was a compliment.", appreciation for what you have (Being Grateful) "You had an argument with your girlfriend? Sir, you HAVE a GIRLFRIEND to argue WITH!"

These are just the three that I've found thus far, the more things that solidify my attention and awareness to THIS MOMENT are what promotes self-awareness.

I'm researching empathy, neurobics (mind exercises to sharpen the mind), intuition, and optimism (turning a bad moment into good one) "I am in pain, don't know why, and that scares me. That I know that I am in pain, don't know why, and that it scares me makes me feel at ease and I may now move to see help with a doctor to find out the cause and acquire the solution." <at this point, starting off positive thinking, when done, feel good and accomplished for having done both the mental work and the physical and came out with both positive aspects in my life.>

Of course, it takes a LOT of work to get where I'm at now, but just by doing little-by-little, cause all things are made of little things, it will all just come together in the end. :3

Good luck! :>

If A = { x of U / x does not belong to x } then A is in A <=> A is not in A OH SHI-

Haskell boobs!

0/1 = OH SHI-!!!

Well the axiom of choice is obviously true, the well-ordering principle is obviously a lie and zorn's lemma could go either way

>>34
yeah...whatever. :\

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ITT: retards who think they are smart but don't know any math.

also, stop caring what other people think of you, it's 4chan ffs.

>>34
lawl

>>37
Speak for yourself, reptile.