Deeper than primes

[HatRack]

HatRack, by your reasoning ("every member is also a set") AND ("{} doesn't have a member") AND ("all members of {} are sets")

See no more

Every member X of {} satisfies P(X) where P(X) is any arbitrary statement about X. This is true precisely because there is no member Z in {} such that P(Z) is false for any arbitrary statement P(Z) about Z. Is that so hard to understand? It's called vacuous truth.

 

[HatRack]

Doron, again... what is it about infinities or 'aproaches' or that a line can be of length 0 that you do not understand?

We never finished that...

And knowing Doron, you never will.

 

[doronshadmi]

Again stop trying to simply posit aspects of your own failed reasoning onto others.

In your case no one (except you) can help you.

For example you asked a question:

So now your “magnitude of existence” can have a negative value?

An example of -1 as a "negative magnitude of exitence" was given.

You simply can't comprehend it.

 

[realpaladin]

In your case no one (except you) can help you.

For example you asked a question:


An example of -1 as a "negative magnitude of exitence" was given.

You simply can't comprehend it.

Doron, the word magnitude describes the size, or for you 'the bigness' of something, not the direction of that 'bigness'.

Furthermore, magnitude is used as an absolute, so a negative magnitude is an incorrect usage of the word.

-1 still has a magnitude of 1 (distance from 0).

 

[The Man]

In your case no one (except you) can help you.

Once again stop simply trying to posit your own limitations onto others. Other people help me all the time.

For example you asked a question:

So now your “magnitude of existence” can have a negative value?

An example of -1 as a "negative magnitude of exitence" was given.

You simply can't comprehend it.

Actually you've got it backasswards as usual …

You asserted…

-1 is a negative existing value, 1 is a positive existing value, 0 is non-negative and non-positive existing value.

No one of these exiting values is "that has to predecessor" (in the absolute sense), which is Emptiness.

Indicating that perhaps your “magnitude of existence” can now have a negative value, so I asked for a direct verification of that indication as…

So now your “magnitude of existence” can have a negative value?

A question you still have not directly answered, perhaps because you simply can’t.

 

[doronshadmi]

Every member X of {} satisfies P(X) where P(X) is any arbitrary statement about X. This is true precisely because there is no member Z in {} such that P(Z) is false for any arbitrary statement P(Z) about Z. Is that so hard to understand? It's called vacuous truth.

"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.

 

[doronshadmi]

Doron, the word magnitude describes the size, or for you 'the bigness' of something, not the direction of that 'bigness'.

Furthermore, magnitude is used as an absolute, so a negative magnitude is an incorrect usage of the word.

-1 still has a magnitude of 1 (distance from 0).

Thank you for agree with me that -1 is an existing thing exactly like 1 or 0.

EDIT:

So now your “magnitude of existence” can have a negative value?

No one of them is Emptiness, which is a concept that The Man can't get exactly becuse he asks about negative existence as a magnitude that is less than Emptiness.

 

[doronshadmi]

The empty set doesn't have a "member" either.

The empty set has Nothing as its member.

Nothing is not a set or a member, but according to ZF "all members of {} are sets".

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

 

[jsfisher]

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

Translation:

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

Not quite, as your equivocation is about to prove.

So we get:

"Nothing satisfies any arbitrary statement about Nothing.

See what you did? You made nothing into something, and then inverted it back on itself. That's equivocation.

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

...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 {}".

And then it becomes gibberish.

Nothing is not a set or a member, but according to ZF "all members of {} are sets".

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

Doron logic -- powerful stuff. Devoid of logic, and that's what makes it so powerful.

 

[doronshadmi]

See what you did? You made nothing into something,

Nonsense.

Nothing is exactly Nothing, and it is already clear all along this thread that you can't distinguish between the name of some notion and the notion itself (exactly as you can't distinguish between "silence" and silence).

EDIT:

Doron logic -- powerful stuff. Devoid of logic, and that's what makes it so powerful.

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.

 

[jsfisher]

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]$$$ \exists x, \, x \in \emptyset \and \neg S(x) $$$[/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.)

 

[doronshadmi]

Not quite, as your equivocation is about to prove.

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

 

[jsfisher]

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

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

 

[doronshadmi]

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.

Nothing is not a member and not a set and Nothing is the best you can get in {}.

 

[jsfisher]

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

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.

Doron, it is very brave of you to accuse others of mistaking names for notions when you continually get it wrong yourself. Please stop being wrong at least some of the time.

 

[doronshadmi]

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.

 

[doronshadmi]

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.


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.

 

[doronshadmi]

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.

"All unicorns" is Something.

Nothing is Nothing.

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.

But you, jsfisher, can't get it.

 

[The Man]

EDIT:

No one of them is Emptiness, which is a concept that The Man can't get exactly becuse he asks about negative existence as a magnitude that is less than Emptiness.

Again who ever claimed any of “them” were your “Emptiness”? Please show were I asked “about negative existence as a magnitude that is less than Emptiness” or stop lying about what was asked and you have yet to answer.

So now your “magnitude of existence” can have a negative value?

 

[epix]

But I am talking about Emptiness, where negative existence (like -1) is not Emptiness, which is something that you can't comprehend by your relative-only view of this subject.


How relative-only view of this subject you have. Emptiness (which is total denial of existence) denials the existence of 1, -1 and 0, and your relative-only view of this subject simply can't comprehend it, exactly as it can't comprehend the totality of fullness, which is beyond collections AND also appears as the non-local property that bridges between localities of a given collection.

It's commendable that your attempt to significantly expand the set theory doesn't neglect every aspect of its historical background.