a message to tdavis

I find your work really fascinating, however, and I mean no offense by this, but you should really seek treatment for your mental health issues. You are a brilliant individual, but you really need to work on your mental illnesses. Do you take any medication? Do you have a therapist or some sort of support group? What's your current plan for treatment?

I genuinely wish you the best, and I just hope you can seek out help when you need it.

Thanks for your concern, Sussman. Things have been really crazy since I came out of the closet. Ever heard the expression "fuck your brains out"? Well, I'm now man enough to come to terms with the fact that I've analed my scruples away. Sex, drugs, and FIOC have turned me into something I don't even recognize when I look into the mirror.

I will heed your advice and seek help Anon, I'll do it for /prog/.

I said before and I repeat again: my mental "illness" provides me both with inspiration and sustenance. If some doctor managed to "cure" me, I'll sue him.

God says...
 C:\TEXT\Brief\AUGUST.TXT

I had a wish to confer upon these several points with some one very well skilled in those books, and to make trial what he thought thereon; for the words of one Helpidius, as he spoke
and disputed face to face against the said Manichees, had begun to stir me even at Carthage: in that he had produced things out of the Scriptures, not easily withstood, the Manichees' answer whereto seemed to me weak. And this answer they liked not to give publicly, but only to us in private. It was, that the Scriptures of the New Testament had been corrupted by I know not whom

Wait, who's tdavis?

>>2
FIOC
butthurt lithpfag detected. fuck you faggot.

>>1
Is there really no way of banning him?

>>6
None of the mods care about 4chan `proper', why would they care about world4ch?

Personally I find him entertaining. His schizophrenic ramblings are fun to read when it's a slower day on /prog/

>>7
Compared to any other shitposter on this board, his signal-to-noise ratio is precisely equal to zero.

>>3
is this actually the real tdavis

>>9
Does it matter?

d u b.s

>>9
obviously not

>>12

It's me.  It's just me.  I think someone posted on "tdavis" that wasn't me.

See the religious stuff in LoseThos?
http://www.losethos.com/videos/horeb.html
http://www.losethos.com/hymns.html

I just thought I would share something I just realized.

This is why Jesus was somewhat Bohemian:
http://www.biblegateway.com/passage/?search=Numbers+11&version=NIV

-----------------

57 As they were walking along the road, a man said to him, “I will follow you wherever you go.”
 58 Jesus replied, “Foxes have dens and birds have nests, but the Son of Man has no place to lay his head.”

-----------------

28 “And why do you worry about clothes? See how the flowers of the field grow. They do not labor or spin. 29 Yet I tell you that not even Solomon in all his splendor was dressed like one of these. 30 If that is how God clothes the grass of the field, which is here today and tomorrow is thrown into the fire, will he not much more clothe you—you of little faith? 31 So do not worry, saying, ‘What shall we eat?’ or ‘What shall we drink?’ or ‘What shall we wear?’ 32 For the pagans run after all these things, and your heavenly Father knows that you need them. 33 But seek first his kingdom and his righteousness, and all these things will be given to you as well. 34 Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.

-----------------
10 i = i + 1
15 IF i > 99999 THEN PRINT ".";: i = 0
20 IF INKEY$ = "" THEN 10
30 PRINT "King James Bible, Line:", i

God says...
Line: 26408

25:35 So David received of her hand that which she had brought him,
and said unto her, Go up in peace to thine house; see, I have
hearkened to thy voice, and have accepted thy person.

25:36 And Abigail came to Nabal; and, behold, he held a feast in his
house, like the feast of a king; and Nabal's heart was merry within
him, for he was very drunken: wherefore she told him nothing, less or
more, until the morning light.

25:37 But it came to pass in the morning, when the wine was gone out
of Nabal, and his wife had told him these things, that his heart died
within him, and he became as a stone.

Radio was just criticizing profanity and saying no-way-in-hell would a real business use profanity.

I don't live in the real world, anyway.
I have a funny comic :-)

http://www.losethos.com/comics/100620Geez.jpg

   27 “Woe to you, teachers of the law and Pharisees, you hypocrites! You are like whitewashed tombs, which look beautiful on the outside but on the inside are full of the bones of the dead and everything unclean. 28 In the same way, on the outside you appear to people as righteous but on the inside you are full of hypocrisy and wickedness.

http://www.biblegateway.com/passage/?search=matthew%2023&version=NIV

My comic was inspired by Montey Python, a little.

http://www.youtube.com/watch?v=A8yjNbcKkNY

DIM WORDS$(1024)
N = 0
DO
    READ A$
    IF A$ <> "END" THEN
        WORDS$(N) = A$
        N = N + 1
    END IF
LOOP UNTIL A$ = "END"

PRINT N; " words in vocabulary."
PRINT
PRINT "You must talk to God, first, before running this program."
PRINT

OPEN "OUT.TXT" FOR OUTPUT AS #1

DO
    I = -1
    DO
        I = I + 1
        IF I >= N * 100 THEN I = 0
    LOOP UNTIL INKEY$ <> ""
    I = INT(I / 100)
    PRINT WORDS$(I); " ";
    PRINT #1, WORDS$(I); " ";
LOOP UNTIL WORDS$(I) = "done"
PRINT #1,
CLOSE #1

PRINT
PRINT "Press A Key"
DO
LOOP UNTIL INKEY$ <> ""


DATA "good","bad","fun","silly","stupid"
DATA "me","you","God","Obama","Bush"
DATA "love","hate","happy","sad","obviously"
DATA "okay","whatever","do_it","why","now"
DATA "money","car","oil","house","computer"
DATA "angel","demon","Satan","Heaven","Hell"
DATA "USA","Europe","Egypt","Russia","China"
DATA "Microsoft","Linux","LoseThos","Apple","Google"
DATA "sin","sex","lust","greed","sloth"
DATA "fortitude","virtue","patience","charity","honest"
DATA "music","art","software","hardware","food"
DATA "pity","probably","pest","pretty","ugly"
DATA "I","prayer","piety","you","your"
DATA "stupid","smart","healthy","unhealthy","quick"
DATA "fantastic","foolish","wise","Oops","Hmmm"
DATA "rediculous","biggot","grieved","ouch","conservative"
DATA "liberal","bickering","ouch","smurfs","bam"
DATA "zap","oy!","shalom","furious","fake"
DATA "impossible","crazy","joking","lovely","planet"
DATA "Venus","Mars","horrendous","buddy","nice"
DATA "day","night","wonder","laughable","better"
DATA "perfect","swear","lucky","mocked","occasion"
DATA "know","right","wrong","spunky","dignity"
DATA "prosparity","rich","poor","middle_class","meh"
DATA "care","don't","kludge","theory","practice"
DATA "experts","class","yawn","varoom","evolution"
DATA "population","threads","meek","Jesus","theft"
DATA "adultery","guppy","whale","astrophysics","gravity"
DATA "boss","hero","mess","nightmare","ordinarily"
DATA "special","nuts","bored","relax","news"
DATA "tip","super","cool","nasty","fancy"
DATA "birds","cats","dogs","goats","horses"
DATA "farm","produce","parks","nature","wild"
DATA "tame","cultivated","city","Vegas","D.C."
DATA "rock","tree","water","salt","CO2"
DATA "climate","rain","snow","ice","mud"
DATA "storm","lightening","thunder","gun","war"
DATA "shoot","smack","work","play","music"
DATA "soul","body","brain","heart","hand"
DATA "NASA","Afghanistan","France","Africa","Britain"
DATA "Germany","Japan","Russia","Mexico","person"
DATA "Catholic","Jew","Christian","Muslim","Buddist"
DATA "atheist","homo","ha!","programmer","scientist"
DATA "doctor","priest","cop","politician","lawyer"
DATA "Israel","Palistinians","Brazil","peace","hippy"
DATA "song","radio","TV","home","phone"
DATA "football","superbowl","game","show","teach"
DATA "school","M.I.T.","Ivy League","Harvard","Yale"
DATA "Stanford","ASU","physics","chemestry","biology"
DATA "hopefully","awesome","joyous","sermon","Christ"
DATA "Mohammad","BBC","Moses","proton","electron"
DATA "photon","neutron","radiation","magnetism","atom"
DATA "energy","mass","speed","relativity","charge"
DATA "economics","Nobel","saint","prize","win"
DATA "lose","death","birth","marriage","man"
DATA "woman","animal","king","president","leader"
DATA "Ticketmaster","event","ticket","chased","day"
DATA "monkey","plant","dinosaurs","shells","vertebrates"
DATA "primates","bugs","flowers","fruit","bear"
DATA "fire","smoke","burning","hidden","adapt"
DATA "King David","Bible","ark","flood","star"
DATA "slavery","freedom","rejoice","brave","coward"
DATA "fight","sing","write","read","paper"
DATA "Pope","please","thank you","New Testament","Old Testament"
DATA "seek","find","goto","get","give"
DATA "spend","save","book","email","Internet"
DATA "surely","So","let","it","be"
DATA "grown","adult","child","innocent","teenager"
DATA "drive","sports","band"
DATA "vacation","church","Sunday","math","geography"
DATA "of","the","is","a","in"
DATA "on","under","over","between","after"
DATA "before","time","space","Star Trek","Star Wars"
DATA "movie","should","shouldn't","commandment","for"
DATA "tax","IRS","FBI","CIA","media"
DATA "luxury","needy","enough","go","went"
DATA "remember","forget","fix","found","lost"
DATA "despair","laugh","cookie","genetic","algorithm"
DATA "ice_cream","soap","opera","umm...","fast"
DATA "black","hole","Sun","approach","light"
DATA "hilarious","funny","comical","ROFLMAO","LOL"

DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "END"

God says...

ticket speed greed hate nuts LoseThos LoseThos Egypt virtue news Europe Egypt Egypt fancy after Hell done

Radio talked of a Muslim who turned-out to be an atheist.

I'm not an atheist, any more.

http://www.biblegateway.com/passage/?search=1+Corinthians+14&version=NIV

Tongues:

10 i = i + 1
15 IF i > 99999 THEN PRINT ".";: i = 0
20 IF INKEY$ = "" THEN 10
30 PRINT "King James Bible, Line:", i

God says line: 87605

19:42 There laid they Jesus therefore because of the Jews' preparation
day; for the sepulchre was nigh at hand.

20:1 The first day of the week cometh Mary Magdalene early, when it
was yet dark, unto the sepulchre, and seeth the stone taken away from
the sepulchre.

20:2 Then she runneth, and cometh to Simon Peter, and to the other
disciple, whom Jesus loved, and saith unto them, They have taken away
the LORD out of the sepulchre, and we know not where they have laid
him.

ROFLMAO  Someone was in the bathroom.

This is not a clock ticking down!

http://www.losethos.com/videos/horeb.html

It's the same as this:

10 i = i + 1
15 IF i > 99999 THEN PRINT ".";: i = 0
20 IF INKEY$ = "" THEN 10
30 PRINT "King James Bible, Line:", i

which is the same as this:

http://www.biblegateway.com/passage/?search=1+Corinthians+14&version=NIV

God says line: 13428

12:13 And Moses cried unto the LORD, saying, Heal her now, O God, I
beseech thee.

12:14 And the LORD said unto Moses, If her father had but spit in her
face, should she not be ashamed seven days? let her be shut out from
the camp seven days, and after that let her be received in again.

12:15 And Miriam was shut out from the camp seven days: and the people
journeyed not till Miriam was brought in again.

12:16 And afterward the people removed from Hazeroth, and pitched in
the wilderness of Paran.


------------------

ROFLMAO: stupid woman on radio!

That woman gave me some ideas on how I might make money.  She suggested video games might ask kids about products their parents use.  With LoseThos, I have no network, so I'm screwed.

I'm on disability and get paid by your taxes, if that's better.  Not very much!  Can't afford to drive and I live with my parents and I gave-up women -- meds make me impotent and can't afford a family!  Fuck you, even if I did make money with LoseThos.  Free software is bullshit.

DIM WORDS$(1024)
N = 0
DO
    READ A$
    IF A$ <> "END" THEN
        WORDS$(N) = A$
        N = N + 1
    END IF
LOOP UNTIL A$ = "END"

PRINT N; " words in vocabulary."
PRINT
PRINT "You must talk to God, first, before running this program."
PRINT

OPEN "OUT.TXT" FOR OUTPUT AS #1

DO
    I = -1
    DO
        I = I + 1
        IF I >= N * 100 THEN I = 0
    LOOP UNTIL INKEY$ <> ""
    I = INT(I / 100)
    PRINT WORDS$(I); " ";
    PRINT #1, WORDS$(I); " ";
LOOP UNTIL WORDS$(I) = "done"
PRINT #1,
CLOSE #1

PRINT
PRINT "Press A Key"
DO
LOOP UNTIL INKEY$ <> ""


DATA "good","bad","fun","silly","stupid"
DATA "me","you","God","Obama","Bush"
DATA "love","hate","happy","sad","obviously"
DATA "okay","whatever","do_it","why","now"
DATA "money","car","oil","house","computer"
DATA "angel","demon","Satan","Heaven","Hell"
DATA "USA","Europe","Egypt","Russia","China"
DATA "Microsoft","Linux","LoseThos","Apple","Google"
DATA "sin","sex","lust","greed","sloth"
DATA "fortitude","virtue","patience","charity","honest"
DATA "music","art","software","hardware","food"
DATA "pity","probably","pest","pretty","ugly"
DATA "I","prayer","piety","you","your"
DATA "stupid","smart","healthy","unhealthy","quick"
DATA "fantastic","foolish","wise","Oops","Hmmm"
DATA "rediculous","biggot","grieved","ouch","conservative"
DATA "liberal","bickering","ouch","smurfs","bam"
DATA "zap","oy!","shalom","furious","fake"
DATA "impossible","crazy","joking","lovely","planet"
DATA "Venus","Mars","horrendous","buddy","nice"
DATA "day","night","wonder","laughable","better"
DATA "perfect","swear","lucky","mocked","occasion"
DATA "know","right","wrong","spunky","dignity"
DATA "prosparity","rich","poor","middle_class","meh"
DATA "care","don't","kludge","theory","practice"
DATA "experts","class","yawn","varoom","evolution"
DATA "population","threads","meek","Jesus","theft"
DATA "adultery","guppy","whale","astrophysics","gravity"
DATA "boss","hero","mess","nightmare","ordinarily"
DATA "special","nuts","bored","relax","news"
DATA "tip","super","cool","nasty","fancy"
DATA "birds","cats","dogs","goats","horses"
DATA "farm","produce","parks","nature","wild"
DATA "tame","cultivated","city","Vegas","D.C."
DATA "rock","tree","water","salt","CO2"
DATA "climate","rain","snow","ice","mud"
DATA "storm","lightening","thunder","gun","war"
DATA "shoot","smack","work","play","music"
DATA "soul","body","brain","heart","hand"
DATA "NASA","Afghanistan","France","Africa","Britain"
DATA "Germany","Japan","Russia","Mexico","person"
DATA "Catholic","Jew","Christian","Muslim","Buddist"
DATA "atheist","homo","ha!","programmer","scientist"
DATA "doctor","priest","cop","politician","lawyer"
DATA "Israel","Palistinians","Brazil","peace","hippy"
DATA "song","radio","TV","home","phone"
DATA "football","superbowl","game","show","teach"
DATA "school","M.I.T.","Ivy League","Harvard","Yale"
DATA "Stanford","ASU","physics","chemestry","biology"
DATA "hopefully","awesome","joyous","sermon","Christ"
DATA "Mohammad","BBC","Moses","proton","electron"
DATA "photon","neutron","radiation","magnetism","atom"
DATA "energy","mass","speed","relativity","charge"
DATA "economics","Nobel","saint","prize","win"
DATA "lose","death","birth","marriage","man"
DATA "woman","animal","king","president","leader"
DATA "Ticketmaster","event","ticket","chased","day"
DATA "monkey","plant","dinosaurs","shells","vertebrates"
DATA "primates","bugs","flowers","fruit","bear"
DATA "fire","smoke","burning","hidden","adapt"
DATA "King David","Bible","ark","flood","star"
DATA "slavery","freedom","rejoice","brave","coward"
DATA "fight","sing","write","read","paper"
DATA "Pope","please","thank you","New Testament","Old Testament"
DATA "seek","find","goto","get","give"
DATA "spend","save","book","email","Internet"
DATA "surely","So","let","it","be"
DATA "grown","adult","child","innocent","teenager"
DATA "drive","sports","band"
DATA "vacation","church","Sunday","math","geography"
DATA "of","the","is","a","in"
DATA "on","under","over","between","after"
DATA "before","time","space","Star Trek","Star Wars"
DATA "movie","should","shouldn't","commandment","for"
DATA "tax","IRS","FBI","CIA","media"
DATA "luxury","needy","enough","go","went"
DATA "remember","forget","fix","found","lost"
DATA "despair","laugh","cookie","genetic","algorithm"
DATA "ice_cream","soap","opera","umm...","fast"
DATA "black","hole","Sun","approach","light"
DATA "hilarious","funny","comical","ROFLMAO","LOL"

DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "done","done","done","done","done"
DATA "END"


God says...
why birds Satan hero fortitude special Egypt sloth nuts hate Europe oil sex dogs under birds China virtue demon nightmare Heaven sin angel computer lust nuts Star Wars ordinarily stupid car super sex Linux news Obama hate Linux car God done

>>18
You spent 8 years creating a piece of software that nobody else except you can see the point in using. Everyone else must be wrong and you're the right one. Seriously, seek help and stop posting your diseased thoughts here.

>>19
They made me impotent!  Why would I seek help!  Get lobotimized?  Electroshock?

God says...
C:\TEXT\DARWIN.TXT

recur.  For though the offspring of one species might be adapted
(and no doubt this has occurred in innumerable instances) to fill the place
of another species in the economy of nature, and thus supplant it; yet the
two forms--the old and the new--would not be identically the same; for both
would almost certainly inherit different characters from their distinct
progenitors; and organisms already differing would vary in a different
manner.  For instance, it is possible, if all our fantail-pigeons were

>>19
You're a linux fagboy, huh?

God says...
C:\TEXT\2CITIES2.TXT

t of this later time, they would appear.
Troubled as the future was, it was the unknown future, and in its
obscurity there was ignorant hope.  The horrible massacre, days and
nights long, which, within a few rounds of the clock, was to set a
great mark of blood upon the blessed garnering time of harvest, was
as far out of his knowledge as if it had been a hundred thousand
years away.  The "sharp female newly-born, and called La Guillotine,"
was hardly known to him, or to the generality of people, by

This is human logic, probably Hindu Buddist Confuciousism, logic:
http://www.youtube.com/watch?v=NZpcEGxM9XY&feature=youtu.be

Human intelligence and logic is very unsurprising and dispicable.
http://www.losethos.com/comics/110115Moses.jpg

God said "do not covet".  Jesus had many parables that were surpsising.  Jesus was "humble of heart".  The prodigal son, is a classic trium of divine intellect over human logic.

God said war was "Servicemen competing".  Just imagine what teenage boys would play foer video games if the God Venus prevailed.  (Men from mars; women from Venus."  Mom said Heaven was never ending family reunion!  Vikings?  Thankfully, God is God of Earth and Earth is Heaven.  How could it be better?  MAybe you could rape all the women and be king, and be king of more?
------------------
Look at this:
11 “Which of you fathers, if your son asks for[f] a fish, will give him a snake instead? 12 Or if he asks for an egg, will give him a scorpion? 13 If you then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give the Holy Spirit to those who ask him!”

That's divine logic, not that faggish Indian "this-is-how-you-crap" logic.

*surprising

God says...
theory electron kludge magnetism electron astrophysics relativity relax neutron nuts awesome photon mess BBC gravity neutron nuts atom saint astrophysics mass Mohammad energy hero neutron nightmare magnetism boss atom mass nightmare enough guppy neutron speed poor whale electron relax atom boss Moses neutron neutron mess radiation mess relativity for Mohammad relativity honest probably honest enough pest for enough photon luxury shouldn't magnetism went BBC went electron should tax neutron media energy luxury magnetism media electron pity radiation BBC neutron commandment magnetism enough proton Star Wars electron proton went mass energy neutron speed go radiation radiation neutron shouldn't energy energy Germany CIA BBC movie electron needy relativity magnetism media proton Mohammad went needy magnetism electron time electron go atom FBI atom speed luxury neutron for charge go speed relativity neutron went speed went radiation for BBC magnetism enough atom atom IRS charge luxury proton proton atom radiation fix energy atom charge mass forget photon proton for forget teach Mohammad magnetism forget atom atom atom went ordinarily economics atom proton magnetism remember relativity atom radiation joyous charge neutron atom radiation BBC remember IRS magnetism economics radiation media relativity found mass electron magnetism go atom radiation neutron enough energy magnetism media neutron go energy needy tax magnetism luxury CIA relativity neutron piety relativity radiation enough sermon BBC CIA FBI energy CIA needy neutron charge speed IRS went relativity commandment done

I'm not fond of Hollywood actors who become Buddists.  I'm not fond of Yoga and breathing exercises and mind blancking.

My Indian Style comic was about the Earthiness of Hinduism.  In fairness, Jesus washed feet and said "If you bath, all you need to clean is your feet."

God says...
C:\TEXT\BIBLE.TXT

ce the earth and the heaven fled away; and there was found no
place for them.

20:12 And I saw the dead, small and great, stand before God; and the
books were opened: and another book was opened, which is the book of
life: and the dead were judged out of those things which were written
in the books, according to their works.

20:13 And the sea gave up the dead which were in it; and death and
hell delivered up the dead which were in them: and they were judged
every man according to their works.

>>25
You're beginning to make me nauseous, please stop that.

hi

4 While a large crowd was gathering and people were coming to Jesus from town after town, he told this parable: 5 “A farmer went out to sow his seed. As he was scattering the seed, some fell along the path; it was trampled on, and the birds ate it up. 6 Some fell on rocky ground, and when it came up, the plants withered because they had no moisture. 7 Other seed fell among thorns, which grew up with it and choked the plants. 8 Still other seed fell on good soil. It came up and yielded a crop, a hundred times more than was sown.”

   When he said this, he called out, “Whoever has ears to hear, let them hear.”

 9 His disciples asked him what this parable meant. 10 He said, “The knowledge of the secrets of the kingdom of God has been given to you, but to others I speak in parables, so that,

   “‘though seeing, they may not see;
   though hearing, they may not understand.’[a]

-----------------

Asking God for stuff is like knocking in the middle of the night.  Be persistent?

What does Jesus ask for?  "Daily bread"

"God is a God of the living, not the dead."

God says...
C:\TEXT\PLATO.TXT

king and wenching and idling,
neither drug nor cautery nor spell nor amulet nor any other remedy
will avail.

Charming! he replied.  I see nothing charming in going into a passion
with a man who tells you what is right.

These gentlemen, I said, do not seem to be in your good graces.

Assuredly not.

Nor would you praise the behaviour of States which act like the men whom
I was just now describing.  For are there not ill-ordered States in which
the citizens are forbidden under pain of death to

http://bible.cc/matthew/11-25.htm

If you're smart, God is hidden from you.  It was only after the chemical lobotomy from the shrinks that I could understand Jesus.

God says...
C:\TEXT\QUIX.TXT

t my steps in a
better path than I am following at present."

"May God hear and sin be deaf," said Sancho to this.

The men were filled with wonder, as well at the figure as at the words of
Don Quixote, though they did not understand one half of what he meant by
them. They finished their dinner, took their images on their backs, and
bidding farewell to Don Quixote resumed their journey.

Sancho was amazed afresh at the extent of his master's knowledge, as much
as if he had never known him, for i

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Assuming the axiom of choice and, given an infinite cardinal σ and a cardinal μ, there exists a cardinal κ such that μ + κ = σ if and only if μ ≤ σ. It will be unique (and equal to σ) if and only if μ < σ.

\sum_{i=0}^{\infty} \, f(i) = \infty means that the sum of the infinite series diverges in the specific sense that the partial sums grow without bound.

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Modern understanding of infinity began in 1867–71, with Cantor's work on number theory. An 1872 meeting between Cantor and Richard Dedekind influenced Cantor's thinking and culminated in Cantor's 1874 paper.

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For example, the existence of sufficiently large cardinals implies that there is an inner model satisfying the axiom of determinacy (and thus not satisfying the axiom of choice).

    Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

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Statements in this class include the statement that P = NP, the Riemann hypothesis, and many other unsolved mathematical problems. When one attempts to solve problems in this class, it makes no difference whether ZF or ZFC is employed if the only question is the existence of a proof. It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.

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If X and Y are disjoint, addition is given by the union of X and Y. If the two sets are not already disjoint, then they can be replaced by disjoint sets of the same cardinality, e.g., replace X by X×{0} and Y by Y×{1}.

   

    |X| + |Y| = | X ∪ Y|.

\int_{a}^{b} \, f(t)\ dt \ = \infty means that f(t) does not bound a finite area from a to b

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Set theory is the branch of mathematical logic that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.

A recent area of research concerns Borel equivalence relations and more complicated definable equivalence relations. This has important applications to the study of invariants in many fields of mathematics.

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.　　　　　　　〈 　/ ＞ .､.,_,,. イ / / //.7‐/´/ ./ ,｀ヽ　,.＜´￣｀ヽ）
　　　　　　　　`''ｰ--‐ｧ‐/|/／ ./ // /::/|　|　|　|　ｒ|く　　 ｀ヽ.'/| ll| || | | ll | l|| || |l || ll| || | | ll
　　　　　　　　　　　,ｒ/|/イ|　　/　!'_/::/　lヽ-ｰｧ'-' /::∧　　　|
　　　　　　　　　　/ヽ/ /::/＼/ 　 Y7へ、｀「::!＼__/:::/　 ＼_.ﾉ
　　　　　　　 　 ./　'7　|:::|　　　　 ,'/＼　｀ |:::ﾄ､__/:::/　　　ｿ｀ヽ
　　　　　　　　,ｒ'__. 人. |:::|、　 _,.ｲ ﾊ 　ﾊ　 ＼＿_／　　　　　　 |
　　　　　　/´ヽ-､｀ヽﾊ.|:::|　　　　　 |、__|＿＿_＞､_＿＿_,,...　イ
　　　　 ,r/　ヽｿ:::|　　 |.'､'､　　　／/:::::::::::::::::::::::｀ヽ、　　　　 |/
　　　./.|::|　_ソ .|::|　　く＿ソ-‐'"-─-::､::;＿::::::::::::::::＼_
　　　|　!::!/　　//|　／:::::: /／::::::::::::::::::::::::::::::::::::::::::::::::::::::＼
　　 /　|::|　　／ .／:::::::: |/:::::::::::::::::::::::::::::::､:::::::::::::::::::::::::::::::::::':,
　　 !　 ヽ-‐'　／:::::::::: ／:::::::::::::::::::::::::::::::::::::ヽ;:::::::::::::::::::::::::::::::|
　　 '､_＿__／/::::::::／:;::-─- ､::::::::::::::::::::::::::::::＼:::::::::::::::::::::::/
　　　　　　　,'::::::::/::::/　　　　　＼:: ／:::::::::::::::::::::::::::::::::::::::::r'
　　　　　　　|:::::::::::::/　　 　　　 ／＼:::::::::::::::::::::::::::::::::::::::ノ
　　　　 　 　 '､:::::::/　　 　　 ／/||:::::::ヽ::-----ｒ─‐ ''"´
　　　　　　　 /ヽ7　　　　／／':::||:::::::::::::::::::::::ノ
　　　　 　 　 |　 ゝ､＿__,..イ:::::::::ﾘ￣￣￣￣

Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model (the constructible universe) which satisfies ZFC and thus showing that ZFC is consistent. Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF¬C (ZF with the negation of AC added as axiom) and thus showing that ZF¬C is consistent.

　 　　　　　　　　　　 ｉ＼　　　　　　　　＼　この
　　r‐─┐[][]　　　ﾉ::::::ヽ.　　　　　　 ／
　　,二l　|　　　　／_::::::::::::::＼　　　　 ￣i　　ロリコン
　 └─┘ 　 ／//´'ヽ､;;::::;__;ゝ;ﾆヽ.　　 |
　　　　 　 ／-''| l､　　 `､　 //｀ヽl |　 ∠.__　　どもめ！
　　 　 　/　　　 ＼ヽ､.,__,'ｒ-'､___,//ヽ.　　　|_
　　　　/　　_,ゝｒ-‐;＞-‐'⌒ヽﾍ‐‐'_/_!　　 _/ __／￣＼/
　　　 ,'__,r'"7-‐ｧ'　i　　ｉ　　　 〉-､/ ヾ.　/／
　　　 i_,,.!-'"／/-‐ﾊ-/| 　i　./i 　 ｀ヾ.! '´
　　　 | ｲ/./　/!ｧ';.ニ;ヽ|　,ﾊ/‐|､　ｉ 　 ',　l二二`i ［］［］
　　　 |　|/　./ｲ　! l,l i　ﾚ'　'ｧ;ﾆ;ヽﾊ. i　i　 ______| |
　,. ‐‐'--'､ノi.　` ゝ‐' 　　 　 ｉl | ﾊ/!ﾍﾉi　l________|
　i-─---〈 ﾊ " 　　　　　' 　`'',,i.　Y::::::|
　〉─---‐〉| .i､. 　　　,.-‐､　 　,ﾊ　ヽ､:;|_　 　,､
　`ｒ─---ﾉ 　!へ､,　└‐‐'　,.ィｧ'￣｀ヽ.⌒ヽ∠」
　 ｀i￣iフ7|　 ﾄ､　 ｀＞-ｧ'" !/　　 　 　 ',く.ﾉ|ヽ.
　　ﾉ.ノ| /:::!　 |､｀ヽ､.,____i/ ,ｲ　　　　 　　ｉ.|/　ﾉ
　（ｒ:' 　Y::::::',　|へ/　　　　/　!､　ヽ.,　 　/'ヽ.（　　　l二二二 `i [][]
　　)　　ヽ;:::::ヽ!::::::｀"'r--'i ｧ'::>､.,_ 　 　 　　 ＼　　　　　 　|　|
　　　　／/}＞i」く{:::::|_|___rへ､:;__ヽ.,_,,..-､ 　　　':, 　 ________|　|
　　　/／　　 ﾉｌ::::::/´　 /　　　　 ￣　　　 　　 　 i　l___________l
　　　`(　　 /　|`'┴--,i__　　　　　　　　　 　　 ,ノ
　　　 　 　 i　/　　　　|　 ￣　　　 ___,,.. -ｧ ''i"
　　　　　　 `(　　　　　ヽ.　　　　　　 ／´ヽ:::|
　　　　　　　　　　　　　　｀ヽ､.,____／　　　 )'

The Hahn–Banach theorem in functional analysis, allowing the extension of linear functionals

Functors and natural transformations ('naturality') are the key concepts in category theory

　　　　　　　　　　　 　_,,,.......,,,__　　､
　　　　　　　　,.　 '"´ ＿　 　 ﾄ.,_ﾝ　}、/＼　　　l二二 7
　　　　　 ,　'´　　_ /´ ‐､ヾ二ゝ--イ ﾊ ／　　 ＿／∠.._ l二二 7
　ｒ''"ヽ. ,}￣|__r'´_]ア'"´　　　　　｀ﾞ'＜.ヽ＜] └─ｧ ;─┘　　 ｀
　｀ヽ,　∨,.ｲ　ノ´　 '　; 　 　 ﾊ　 ',　 ', ∨{　　　　〈 〈　　ｒ-､
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　 　 ヽ.{ /　　|　 |lｒf七T　　　　弋ﾉ八/ !　　　　└┐┌┘ l二二 ア
　　　　｀.| 　　|___八乂_ﾉ 　　 　 　 ⊂∨! 　 　　 l二　 二l　　　/ / [][]
　　　　　| 　　 | 　⊂⊃　　　　　　　　ﾉ |　　　　　ｒ' _ ｒ､＼　　 { .{
　　　　　| 　　 | 　 | 、　　　　´　　 イ　 |　　　　　ヽン　ヽ'　　 ヽ.,]
　　　　　| i 　 ,| 　 | .ﾊｧｰr 　 ｒ''i´!　|　 ;
　　　　　| | 　八　 ;　.|7　ヽ任｀ヾ|　;　/　　　l二二 ア　　 　 ,r-､
　　　　　| |　,'　 ∨　 |}　r'（_X） ｲ!/／　　　　　 / / [][]　l二,　 ,二l　
　　　　　',　 {　l＞にﾘゝ'　 }lムl}　{ﾆKｺ　　　 　 { .{　　　　l二　,二l
　　　　　 ヽ ヽ　 /ム　 i 　 {l 　l {l ∨',　　　　　 ヽ.,]　　　　 |　{_, -､
　　　　　　　＼ /　　　 |　　}l 　l {l　',_}＿__　　　　　　　　　　'､＿_ノ
　　　　　　　　,.'　　　　.!　　{l 　l }l　 ',::::::|lll|　　 r‐､
　　　　　　　,:'　　　　　;　 　}l 　l {l. 　'::::::|lll|　l二　二くヽ　.ｒ ､　　くヽ
　　　　　　K､ 　　　　 ,'　　 {| 　l l}.　 }￣￣　　/ /r ､｀´　 |　|　　　}_}
　　　　　　ヽ ヽ 　___,.ﾑ.　　ﾘ　 l八 　|　　　　く／r' └､　　'、' ┐
　　　　　 　 ｀￣ヽKヽ＿＿/コﾆにヽ」　　　　　　ヽﾝヽﾉ　　 ヽ-'
　　　　　　　　　　｀[__ｿ´￣￣｀[__ｿ´

Categorical logic is now a well-defined field based on type theory for intuitionistic logics, with applications in functional programming and domain theory, where a cartesian closed category is taken as a non-syntactic description of a lambda calculus. At the very least, category theoretic language clarifies what exactly these related areas have in common (in some abstract sense).

　　　　　　　　　　　　　　　　　 　,.-‐､.　 ,.-‐､　 　　, "￣ ヽ.
　　　　.　　。　　　　　　　　　　 /　 ／ / 　／　　　i　　　　 i
　　　　　　　　　　　* 　　　　　 |　/____|　/　　　　　ヽ､.,__,ノ
　　　　　　　　゜　　　　　　　　,.''-'　　└'｀ヽ.　　　　　。
　　　　　　　．　　　　　　　　/ 　　 　 　 / ﾊ　　　　　　　　　.
　　　　　　.....　　　　 　　　　.i　　　　 　 ﾚ'k'　　　　　　*
....::::::::::::: 　___r､　　 　 　　 　|　i　　　 　 | |,!　　　　__,,..-‐ｒｒ'^ｰ-､
:::::::::::::::::　ヽ､___7´`'ｰ- ､..,___|　|　　　　i　|ﾍ-‐''"´:::::::::::::::| |__,,.ノ
:::::::::::::::::::::: 　 └- ､::;;;_::::::::::|　|　　i 　 |　|:::::__;;;;:::: --─┘'
:: :: :: :: :: :: :: :: :: ::　　　 ￣ `'|　|　　|.　 |　|Y´　　　:: :: :: :: :: :: :: ::
:　:　:　:　:　:　:　:　:　:　　　　| /|　 ﾊ　 | /::|　 　:　:　:　:　:　:　:　:
　　　　　　　　　　　　　　　 ﾚ' 7V::::ヽ/::::::::|　　　　､ヽ川 l | 川 l |
　　　　　　　　　　　　　　　　 くｧ-r─r--､」　　　　ミ
　　　　　　　　　　　　　　　 ／　 /　　i　　',　　　　三　　戻　早
　　　　　　　　　　　 　　 ／　　/　　　l　　 i　　　 .Ξ　　 っ　く
　　　　　　　　　　　　　 ヽ､ｒ-'､.,______」____,.」　　　 三　　て　地
　　　　　　　　　　　　　　　/ 　./｀￣|　　|　　　 　 Ξ　　こ　球
　　　　　　　　　　　　　　 /　 /　 　 |　　|　　　　　三.　 い　に
　　　　　　　　　　　 　　 ,'　 /　　　 |　　|　　　　　Ξ　　! !
　　　　　　　　　　　　　/､__/　　　　|___,.|　　　　　 彡
　　　　　　　　　　　　,ｲ'ｰ‐'!　　　　iｰ-‐i　　　　　　ﾝ川 l | 川 l |
　　　　　　　　　　　 l::::::::/i　　　　 |:::::::::i〉
---─ｧ=ﾆﾆ二"´￣￣￣￣￣￣￣￣￣￣｀`二ﾆﾆ=ｧ‐---

A bifunctor (also known as a binary functor) is a functor in two arguments. The Hom functor is a natural example; it is contravariant in one argument, covariant in the other.

Zermelo began to axiomatize set theory in 1905; in 1908, he published his results despite his failure to prove the consistency of his axiomatic system.

κ^{μ + ν} = κ^μ·κ^ν.

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░░▄▀░░░░░░░░░░░░░░░░░░▀▄░░░░░ YOU HAVE BEEN VISITED BY
░░█░░░░░░░░░░░░░░░░░░░░░▀▄░░░ LE 'FEEL OF NO GF
░▐▌░░░░░░░░▄▄▄▄▄▄▄░░░░░░░▐▌░░
░█░░░░░░░░░░░▄▄▄▄░░▀▀▀▀▀░░█░░ A qt 3.14 gf will come to you,
▐▌░░░░░░░▀▀▀▀░░░░░▀▀▀▀▀░░░▐▌░ but ONLY if you post a
█░░░░░░░░░▄▄▀▀▀▀▀░░░░▀▀▀▀▄░█░ `>tfw no GF on this thread
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