Deeper than primes

[jsfisher]

It's that reading comprehension thing again, isn't it? I said nothing of the kind. (Pun intended.)

Worng.

This is exactly what you wrote:

Not quite, as your equivocation is about to prove.

You said "nothing of the kind" maybe in your dream.

Yes, definitely a reading comprehension problem, and a sequential reasoning failure as well.

I said "as your equivocation is about to prove", but that is totally unrelated to the Axiom of Empty Set. In no way did I even hint the axiom required proof. Moreover, the use of the verb, to prove, in this case carries the meaning of to show in a definitive way. The referent of what was to be shown in a definitive way is your equivocation of the word, nothing. You used it in at least two ways as if they were the same.

Classic equivocation. To continue to equivocate intentionally goes by a less kind verb, to lie.

 

[jsfisher]

By the way, this is yet another example of your sloppy abilities of thought and of expression. The empty set is not nor has it ever been an axiom. There is an axiom in ZFC that takes the empty set as a given, but the empty set itself is, not surprisingly, a set.

Again you play with words, the exitence of {} is axiomatic by ZF so its emptiness (Nothingness) is not proved.

What does this have to do with the point I raised? Is your inability to actually follow a conversation willful? It does appear deliberate.

You said:

So, according to jsfisher's twisted reasoning {} is not an axiom anymore, because now we have to prove that there is Nothing in {}.

So, according to Doron, the empty set is an axiom. Are you really claiming the empty set is an axiom?

 

[jsfisher]

You'd get the same sort of ridiculous conclusion by misinterpreting "All unicorns are pink". In Doronese, that would be "nothing is pink."

This is your ridiculous reasoning.

No, that is me applying your ridiculous reasoning. There are just as many unicorns as there are members of the empty set. So, any bit of illogic you apply to members of the empty set is equally applicable to unicorns.

 

[jsfisher]

Nothing is not a set or a member, but according to ZF "all members of {} are sets" (Or by jsfisher's words: "Every member of {} is a set, without exception" ( http://www.internationalskeptics.com/forums/showpost.php?p=6713481&postcount=13621 )) .

In other words, ZF does not follow its own determination.

By the way, Doron, why do you continually repeat this bit of nonsense? Aside from it being spam that could draw the attention of the forum moderator staff, it really doesn't advance any sort of intelligent argument.

It begins with an ambiguous reference to something you are calling "Nothing", but that part has no apparent relationship to the statement that follows, viz. that all members of the empty set are sets. Then, somehow out of the blue comes the unsupported conclusion that ZF does not follow its own determination.

Do you imagine some chain of logic connecting the first two to the third?

 

[jsfisher]

I made a minor error in this post, below. I noticed the error right at the 120 minute time limit, and my attempt to correct it in-line made it worse. Here is the corrected version. The third expression should have been an and relationship, not implication:

Here's the original proposition:

[latex]$$$ \forall x, \, x \in \emptyset \Rightarrow S(x) $$$[/latex]​

where S(.) is the "is a set" operator.

Now, Doron, if you wish to prove this proposition false, attempts at cute word games do not accomplish this. Instead, you need to establish the negation of the proposition as being true:

[latex]$$$ \neg \forall x, \, x \in \emptyset \Rightarrow S(x) $$$[/latex]​

Through the miracle that is Mathematics, we can simplify this into:

[latex]$$$ \exists x, \, x \in \emptyset \wedge \neg S(x) $$$[/latex]​

So, all that is required to prove the initial proposition false is for you to exhibit just one example of an element of the empty set that isn't a set. (And it doesn't count if you just make something up that may be true in Doronetics, but isn't in real Mathematics.)

 

[epix]

Originally Posted by HatRack

[latex]$$\sqrt{2} = \left \{ x \in Q : x^2 < 2 \lor x < 0\right \}$$[/latex]

Doron, your complete misunderstanding as to what this mathematical statement means is... I simply have no words.

On the contrary, you are using too many words and notations, until you do not understand the notions at the basis of them.

I guess you would have to ask HatRack for

Pi = S = { ? }

or some esoteric real to prove your statement. The fallacy of that kind of proof seems to reside with you: how do you find out that HatRack possibly messed up?

Dedekind and others were trying to show that the real line doesn't have gaps due to the absence of some irrational numbers. Log x or sin x, for example, is not the construction of irrational numbers -- these are functions.

Here is something you should play with to get your hands dirty at least once: The sum of finite sequence of rationals is always a rational number. But the sum of some sequences of rationals whose value decelerate without bound results in the limit that is an irrational number. For example, the convergent series

1/1! + 1/2! + 1/3! + 1/4! + ...

has limit e, the base of natural logarithm. So this is the way irrarationals are constructed, but there is a long way from this example to Dedekin cuts. It's a difficult math when you don't get your hands dirty before you hit the subject.

 

[epix]

The devil shall appear six times in 2011!

Nonsense.

No, wait. The notorious devil number is 666 and the devil is supposed to appear 6 times? That's kind of coincidental, isn't it?

We must think now . . .

Are you thinking? What? It doesn't go well?

Oops. Sorry. Here we go . . .

Doron, look at the ending of the prophecy: The devil shall appear six times in 2011!.

What is 2011! is meant as the factorial of number 2011?
http://en.wikipedia.org/wiki/Factorial
That would be a big number... youknowwhatimean?

2011! =
7019154933932541646101737582908803945572530877243757385056323465293927907427714999157897285305954475529003205812842103027692844793201600116178597847919162690527445889909411699177912942493530614309971469412410582395243475561919023910382142739418002351410552809248890274414164605218131232505450096502695984505407003424277521984226996082905298527405589822798403824034876431921606727025623060058051750792154655115456128678857131643906837462422913158229683914870037614978977409456596765132530050589613016668508668175675954619987615221274556960916991469318488185373335417022978102144873703186605987991405043555713243383607782597736923221968325224366511563170180536643129159235362727924965649090416611672237548645883419198830643754779033496685056750242739499891538629121513924162270705129346678078572863528337287460837823081975103192023773430657385220642597116854180076869639708715557011126648619998351003756590936330542740005553009542232459848780175977935718419139308587870729008197833064935050811524346575341140047878453948319237833386163838229783533413309062231167519211520797426444496458350792337464575267327023128276286372498758847450042442988682724010616527410225206443981973311707352352113654091841925963096864954267107243345950268971372609522064057377117471268132568179053333973883242679797496847493153325065695526730601452376612513386331076551243362657498121845599732535902647580674687605257626584137699410394528648877551012771702801004115613281201662514748230582160939608409012861244657377152826814227501059576109098213491257945580069599290481697899670301069564047670406926993981864809273523827134249254814727834941600494043443181501051613152266962607425808262495964130068026537277034475399195442813972544927400167375471506973553532490099218563998241599456294517890550165684449359156503199959304384675297274286826324962472419813258697814930084086177207274834760758942772614094846275295125468448050223478346453664211930368054487108704016201731114335245020845018269841128229413637094730135553651872267311898225594962380551033630073142524004255271898426281204609001826028970045284815562362620782073297861047564212359731077071396895849117840948634036043519275221724140794927037733544695696659407047150806730181524297459824229037684382710923349385073739173991245903450162368488081781738854768420362374456492513769816043152460183401110844826499511247069701883400141184794915716189383860123979826776062917514592456939691241935854281028749514682942164646039744736546401326883610920485751005123569625099959395119845677665587293064148552629058638650747399908966054109379921926905392232424084426423136654664334434493633437462425678046218738775759474611443802580262224688340785671601216805140119214122901414708950755526713227227134040545956746437132390333764629136600866679593273339559689638194472417276519108960306127833524866816084380007381440432218634488536311929302234919229850323819580866447817089494027377141196787932650224121268212252066576782254830131983111187567068668504297284005249300851840856320706369863899699297648906677437384063525779744168484405791000715811849439662422205937242038073427019984175061274267787792252204381230628888572707934050389609057172694615936075109036307527119549300239026399084614159598379027608901705481701323152462684466717403820413461301770805670023214674600957484703911343003751045232622799816641220667184608980951638926865463791080384800635291339728232583637459121479958358481434216259573864059316907459524156018670248065339532410926004807216067358141821719506257562864120425384506400853893340821724128641671368422957498416270464605801373668235018154233819427342987011185170530948377613110053782644634729938687445376570621121930608041412600718497392845534937793367356104269365799806013403062737400159618768176915803612434671227264327196992524206313450198379396351696718010061176779283143874811881877180054351914491111150007193658625830111500737428482687539151033135941600574440965143992477748683865551891801802624199055661190861604506709595898242420806509929828436411008410923454373741523845424966258220188212235513590751870305482230112964482529559435730255459915492885376984613551068406617905241935727677579914198480185756668508668175581384061380375147353013218774783929882309682151966213569142526758579120229573599058798639694880006262008712780372052440332374425668250780706886596174361105215697797726854457496951831424247229665618540408965798247479535818776515642026574804805498414565476251271077131461354934978176730468255312211942427128615880381405178257422890430706539200145952300461269144312301507389181119194429997835421674722860581301205075675307225584165157639631520226035140338622270143248977909156649198507519978066025557045059392111813420752211309161585574424642608256066696408182483650718142321331032965280472938478710053031536621717163842367901487157587990249781830567259184438744912921104902536643869598792884176996493072073150735751004732571317365480039028953749419426924532172973885482210305819662840597725855952567789294006522599486781217317497153434512336894624517145457641510889743445607178661587813040562903866687113284821837406960710916774826537816167704857664485813244391088394846427882133822055105081794612247568254551681061396896664980939006439980307979090139867832156584662016236364622984157840563858856764971679744000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

See? 666 showed up exactly 6 times in 2011!

I leave the easy part regarding the actual dates and places of the devil's appearance to you.

 

[HatRack]

"Every member X of {} satisfies P(X) where P(X) is any arbitrary statement about X"

Translation:

"Nothing" = "Every member X of {}"

So we get:

"Nothing satisfies any arbitrary statement about Nothing. Since there is Nothing in {} such that Nothing is false for any arbitrary statement about Nothing, then we can conclude that it is true that there is Nothing in {}".

EDIT: Nothing is not a set or a member, but according to ZF "all members of {} are sets" (Or by jsfisher's words: "Every member of {} is a set, without exception" ( http://www.internationalskeptics.com/forums/showpost.php?p=6713481&postcount=13621 )) .

In other words, ZF does not follow its own determination.

Doron, I've got to say, I'm quite surprised that you're struggling with vacuous truth so much. I mean, after all, that is what the entire field of Doronetics is based upon: If false statement, then false statement.

 

[epix]

Doron, I've got to say, I'm quite surprised that you're struggling with vacuous truth so much. I mean, after all, that is what the entire field of Doronetics is based upon: If false statement, then false statement.

There is a possibility -- even remote one -- that Doron has a difficulty to understand this.

"Every member X of {} satisfies P(X) where P(X) is any arbitrary statement about X"

Perhaps he wonders about where the heck the empty set of a power set comes from. Given set

A = {a,b}

there is a question mark regarding power set

P(A) = { {},{a},{b},{ab} }

where {} is not decidedly a subset of A, but Cantor listed it as such. Why?

An empty set is a subset of a set by definition, but is this property entirely of arbitrary nature or is there a reason hanging somewhere? If the definition is based on arbitrary decision, why not to exclude arbitrarily the empty set from being the subset, which would make more sense, given the set A.

Perhaps Doron would figure out this set theory problem given his expertise with Fullness and Emptiness: There is a case (set) of bottles containing white and red wine. We separate them according to the color -- we put the bottles with red wine into a red bag and the bottles with white wine into a white bag. Now we have two subsets and the question is: Which bag contains the bottle which is empty?

(Clue: Before the separation, all bottles were full.)

 

[doronshadmi]

Doron, I've got to say, I'm quite surprised that you're struggling with vacuous truth so much. I mean, after all, that is what the entire field of Doronetics is based upon: If false statement, then false statement.

I am not surprised that you swallow everything without first checking it, like any dogmatic thinker.

 

[doronshadmi]

Are you really claiming the empty set is an axiom?

Let us put it this way: {} is an axiomatic fact under ZF so Nothingness is not proved.

jsfisher you have a poor tenancy to ignore already clarified things, and run after their pre-clarification state.

 

[HatRack]

I am not surprised that you swallow everything without first checking it, like any dogmatic thinker.

What is logically wrong with this statement:

Every member X of {} satisfies S(X) where S(X) is any arbitrary statement about X.​

Or, in its formal form:

[latex]$$$ \forall x, \, x \in \emptyset \Rightarrow S(x) $$$[/latex]​

 

[doronshadmi]

No, that is me applying your ridiculous reasoning. There are just as many unicorns as there are members of the empty set.

So please show us some unicorn, which is a set.

If you can't do that you are left with Nothing, and Nothing is not a set and not a member, or in other words, {} does not follow ZF determination, which asserts that "all members of {} are sets".

 

[doronshadmi]

What is logically wrong with this statement:

Every member X of {} satisfies S(X) where S(X) is any arbitrary statement about X.​

Or, in its formal form:

[latex]$$$ \forall x, \, x \in \emptyset \Rightarrow S(x) $$$[/latex]​

Translation:

"Nothing" = "Every member X of {}"

So we get:

"Nothing satisfies any arbitrary statement about Nothing".

 

[doronshadmi]

By the way, Doron, why do you continually repeat this bit of nonsense?

Because it is not nonsense.

Aside from it being spam that could draw the attention of the forum moderator

It is a spam if you get it, and then a repeat on what you already get.

But this is not the case jsfisher, because you do not get it.

 

[HatRack]

Translation:

"Nothing" = "Every member X of {}"

So we get:

"Nothing satisfies any arbitrary statement about Nothing".

That's not what I asked. I asked for you to point out the logical flaw in the statement. Please see http://en.wikipedia.org/wiki/Formal_fallacy to understand what a logical flaw is.

 

[HatRack]

So please show us some unicorn, which is a set.

If you can't do that you are left with Nothing, and Nothing is not a set and not a member, or in other words, {} does not follow ZF determination, which asserts that "all members of {} are sets".

We, as in everyone else who posts here but you, do not need to see a unicorn. You are the only one who does, because you fail to understand jsfisher's statement that there are just as many unicorns in existence as there are elements in the empty set.

 

[doronshadmi]

It begins with an ambiguous reference to something you are calling "Nothing",

Nothing can't be understood as "Nothing", which is Something (an existing name) (and you simply can't comprehend this notion)

but that part has no apparent relationship to the statement that follows, viz. that all members of the empty set are sets.

Exactly, Nothing can't be considered in terms of members or sets, and this is exactly the reason why {} does not follow ZF determination, which asserts that "all members of {} are sets".

 

[doronshadmi]

That's not what I asked. I asked for you to point out the logical flaw in the statement. Please see http://en.wikipedia.org/wiki/Formal_fallacy to understand what a logical flaw is.

HatRack please explain what is exactly Every member X of {}?

 

[doronshadmi]

because you fail to understand jsfisher's statement that there are just as many unicorns in existence as there are elements in the empty set.

jsfisher simply uses a twisted way for Nothing.