Is religion dying?

[viole]

What is described for the empty-set as a subset is not logic. No. It's a definition.

So, the professor was wrong when he said: the way to see why it’s true (that the empty set is a subset of any set is…..? Because that is to me a proof, not a definition. A proof by contradiction.

he must be completely deluded to offer a proof of something that is, according to you, totally wrong in a book called “the book of proof”.
how can he be so stupid?

ciao

- viole

 

[viole]

No, I'm not.



Bash with some powershell helper scripts.

powershell? Windoze?

No python? Schade. That would have helped you with your problems understanding sets.

ciao

- viole

 

[dybmh]

So, the professor was wrong when he said: the way to see why it’s true (that the empty set is a subset of any set is…..? Because that is to me a proof, not a definition.

No, it's not a proof. You want it to be proof, but, it's not. At best it is vacuous-proof. But vacuity is not in that book as far as I can tell.

he must be completely deluded to offer a proof of something that is, according to you, totally wrong in a book called “the book of proof”.
how can he be so stupid?

He didn't offer it as a proof. He is bringing a definition. It's a book about proof, not a book of proofs.

 

[viole]

He didn't offer it as a proof. He is bringing a definition. It's a book about proof, not a book of proofs.

i love this, i could do this for the next 10,000 posts

Exactly. He defined what a subset is. He defined what an empty set is. And proved that, according to those definitions, the empty set is a subset of every set. That is what the entire “to see why it is true …..”, means. To show why something is true is a proof, not a definition. Namely To show that, according to those definitions, the empty set is a subset of every set.

i mean, it is black on white for everyone to see. If you do not see that, you are seriously in denial.
or please show us that he defined the empty set as being a subset of every set, instead of showing us why it is the case.

ciao

- viole

 

[dybmh]

powershell? Windoze?

Sadly that is only option for the practice management software.

No python? Schade.

Why NOT bash?

That would have helped you with your problems understanding sets.

There's no problem understanding for me. Your so-called logic is primitive. It doesn't do understading. It has no understanding. It cannot evaluate relevance nor evidence. Both are required for understanding.

Here is a fact.

In classical logic, particularly in propositional and first-order logic, a proposition

is a contradiction if and only if

.

Contradiction - Wikipedia

en.m.wikipedia.org

If you don't know any Jews, then All the Jews you vacuously-know are simultaneously atheists and not atheists.

That's a contradiction.

So, is it a contradiction? If not, why not? If so, why are you considering it true? Are you even talking about Jews?

 

[dybmh]

i love this, i could do this for the next 10,000 posts

Great!

Exactly. He defined what a subset is. He defined what an empty set is. And proved that, according to those definitions, the empty set is a subset of every set. That is what the entire “to see why it is true …..”, means. To show why something is true is a proof, not a definition. Namely To show that, according to those definitions, the empty set is a subset of every set.

BUZZZZZZZ! Nope, that is incomplete and false.

"And proved that, according to those definitions" is incomplete and false.
"And declared that, according to half the definition, that the emptyset is a subset of every set." is complete and true.

i mean, it is black on white for everyone to see. If you do not see that, you are seriously in denial.

No, you're cherry picking. He clearly says, it can be seen to be true by looking at the last sentence. So that's all you can say.
I can easily say, the first sentence shows the opposite.

or please show us that he defined the empty set as being a subset of every set, instead of showing us why it is the case.

Sure. I already did. Here it is again, in black and white. All that is *actually* given is half the definition, and then a proposal is made that it can't be shown this half of the definition isn't true. But this ignores the first sentence, and it can't be shown that it's not true either.

I think what you're missing is: if everyone is using the same language, they could all be copying the same source, and all making the same error. Again, this is called social intertia. I already provided a link on it.

people are encouraged to "accept the social world [ mathematic conventions ] as it is, to take it for granted, rather than to rebel against it, to counterpose to it different, even antagonistic, possibles." This can explain the continuity of the social order [ mathematic conventions ] through time.​

​

Social inertia - Wikipedia

en.m.wikipedia.org

​

Anyway, here's the statement from the book. It clearly shows that only the last half of the definition is consulted.

 

[dybmh]

@viole,

This is the *actual* definition of a subset.

A(x) ⊆ B(y) if ∀A(x):{x ∈ A(x) → x ∈ B(y)}

That's it. It's a defintion.

"→" means "~{x ∈ A(x)}" is completely irrelevant, because "→" is defined that way.

But "→" does not describe the relationship between unknown Jews and their atheism/theism.

"→" means "suppose" or "assume it's true"

If Jews are unknown, there is NO reason to suppose or assume anything.

And that's why this fails. There might be occasion when it makes sense to assume it's true unless it's proven false. This isn't one of them.

But the point is:

​

"A(x) ⊆ B(y) if ∀A(x):{x ∈ A(x) → x ∈ B(y)}"​

IS NOT:

​

"Suppose A and B are sets. If every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is not true that every element of A is also an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B."​

It is *actually* this:

​

Suppose A and B are sets, and assuming that it's true that every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is proven that an element of A is not an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B.​

See the difference?

This is detailed in the PDF after chapter 1 under conditional statements. In that section, it makes the comparrison where the assumption is: "Assuming you pass the final exam, you will pass the course." But, they say, if you don't pass the exam, the teacher might choose to pass you anyway. They could make that executive decision to bypass the defintion of the final exam.

But in this case, you cannot make the executive decision to change the meaning of Jew, Atheist, and Theist, such that a Jew can be both Athiest and Theist simultaeously. That's why my proof works, and it works for any set, any property, any proposition, excluding its indentity.

Anyway, you need to advance past chapter 1. Advancing past chapter 1, changes the definition of a subset into an "assume it's always true" defintion. But belief in a god or gods, is NOT an assume it's always true definition.

Okie, dokie?

 

[viole]

Great!



BUZZZZZZZ! Nope, that is incomplete and false.

"And proved that, according to those definitions" is incomplete and false.
"And declared that, according to half the definition, that the emptyset is a subset of every set." is complete and true.



No, you're cherry picking. He clearly says, it can be seen to be true by looking at the last sentence. So that's all you can say.
I can easily say, the first sentence shows the opposite.



Sure. I already did. Here it is again, in black and white. All that is *actually* given is half the definition, and then a proposal is made that it can't be shown this half of the definition isn't true. But this ignores the first sentence, and it can't be shown that it's not true either.

I think what you're missing is: if everyone is using the same language, they could all be copying the same source, and all making the same error. Again, this is called social intertia. I already provided a link on it.

people are encouraged to "accept the social world [ mathematic conventions ] as it is, to take it for granted, rather than to rebel against it, to counterpose to it different, even antagonistic, possibles." This can explain the continuity of the social order [ mathematic conventions ] through time.​

​

Social inertia - Wikipedia

en.m.wikipedia.org

​

Anyway, here's the statement from the book. It clearly shows that only the last half of the definition is consulted.


View attachment 78061

And? Of course we need to define things before proving other things. And in this case, according to the definition of subset, and the definition of empty set, he proved the empty set is a subset of every set. He said himself: look at the definition of subset, and the rest is trivial. This is a necessary conclusion from the definitions. That is what he wrote. Black on white. For all to see.

what else do you need apart from reading what you sent us? And what is so difficult to understand?

Ciao

- viole

 

[viole]

Suppose A and B are sets, and assuming that it's true that every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is proven that an element of A is not an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B.

Therefore, if A is the empty set, then A is not a subset of B (your claim until now), because there is at least one element of A that is not an element of B (your point here).

What element might that be? LOL

Not only you post files that make my case, thinking they make yours, but now you start posting yourself things that actually make my case, and defeat yours.

Ciao

- viole

 

[dybmh]

And? Of course we need to define things before proving other things.

You didn't do that when you claimed all the Jews you know are atheists. And you didn't do that when you claimed that married-bachelors have blue hair. Nor anytime you've tried to "prove" that some non-existent thing obtains an existent thing.

And, you don't include "vacuous" in the statement.

And in this case, according to the definition of subset, and the definition of empty set, he proved the empty set is a subset of every set. He said himself: look at the definition of subset, and the rest is trivial. This is a necessary conclusion from the definitions. That is what he wrote. Black on white. For all to see.

Nah, it was a restatement of half the definition, not a proof.

what else do you need apart from reading what you sent us? And what is so difficult to understand?

I understand perfectly. Page 12 is the beginning, and you haven't moved beyond it.

 

[viole]

V

I understand perfectly. Page 12 is the beginning, and you haven't moved beyond it.

do I need to? Or are you postulating that this professor proved something that can be defeated by what he writes a few pages afterwards? No sane professor would do that.

in fact, mathematicians are not like Bible believers. We usually drop in the garbage bin any mathematical book that shows absurdities after the very first pages.

anyway, you proved that the empty set is a subset of every set yourself. So, the rest is irrelevant.

ciao

- viole

 

[dybmh]

Therefore, if A is the empty set, then A is not a subset of B (your claim until now), because there is at least one element of A that is not an element of B (your point here).

But since that ^^ wasn't the definition that was *actually* given, it is a restatement incorporating the information given in chapter 2, then what was said in chapter 1 isn't *actually* a proof of the defintion given in chapter 1.

And then using the method in chapter 1 to try to prove anything is erroneous because it doesn't actually prove anything.

What element might that be? LOL

The ones spoken about in definition 1.3.

Not only you post files that make my case, thinking they make yours, but now you start posting yourself things that actually make my case, and defeat yours.

No, my case is:

The actual defintion of a subset ASSUMES that every set is a subset of every set. That's pretty stupid. But, that's the definition.

Your claim that All the Jews you know are atheists is relying on the same assumption, but that assumption is omitted.

In order to *actually* bring a true statement, it ould need to be written:

Assuming that all Jews are atheists, All the Jews I vacuously-know are athests, since I don't know any Jews.

Now it's true, because the irrational assumption is declared.

Of course we need to define things before proving other things

You didn't define the statement as an assumption that All Jews are atheists.

 

[viole]

It is *actually* this:
Suppose A and B are sets, and assuming that it's true that every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is proven that an element of A is not an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B.
See the difference?

Your words.
are you reconsidering them?

ciao

- viole

 

[dybmh]

do I need to?

Sure, you need to read past page 12.

Or are you postulating that this professor proved something that can be defeated by what he writes a few pages afterwards? No sane professor would do that.

It's not a proof.

And yes, I think the profesor did omit the details of the actual defintion because it would distract and confuse a beginner. But if, the beginner never reads past page 12, as you are attempting to do, they will never know anything past... ummm... page 12.

in fact, mathematicians are not like Bible believers. We usually drop in the garbage bin any mathematical book that shows absurdities after the very first pages.

In fact you are acting like a bible believer.

anyway, you proved that the empty set is a subset of every set yourself. So, the rest is irrelevant.

No, it's just a definition based on the assumption that every set is a subset of every set. Then without being able to prove it's false, it vacuously-is true.

It's empty-being... vacuous-is... a contradiction.

As I showed you before, there is NO empty-set in classical logic. There is a convention to accept the empty-set, but it's not actually empty.

But this is acomplicated idea, and you do not seem to be able to grasp it. That's OK. But you will make nonsense false conclusions as a result. And you will fail at writing proofs and theorums if you don't define things properly. And you'll never notice those faults, if you cannot move past chapter 1 in an entry level book on the subject. In addition to that moral bankruptcy reduces the odds that any other erro checking capabilities will be empoyed when making false statements. And... sadly your methods don't include any tools for evaluating relevance or evidence. So that also reduces the odds of being able to error check what you say or write.

All in all, ignorance is virtually assured for you.

 

[dybmh]

Your words.
are you reconsidering them?

ciao

- viole

No, it's a proper definition. But it is omitted from Chapter 1. It's silly to make that assumption that every set is a subset of every set. And it's equally silly to apply that assumption to All the Jews I know are atheists.

That's where you fail, again, and again, and again...

 

[viole]

IS NOT:
"Suppose A and B are sets. If every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is not true that every element of A is also an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B."
It is *actually* this:
Suppose A and B are sets, and assuming that it's true that every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is proven that an element of A is not an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B.
See the difference?

Your words.
are you moving away from them?

ciao

- viole

 

[viole]

No, it's a proper definition. But it is omitted from Chapter 1. It's silly to make that assumption that every set is a subset of every set. And it's equally silly to apply that assumption to All the Jews I know are atheists.

That's where you fail, again, and again, and again...

nobody is making that assumption. A pretty silly claim, actually.

So, you stand by them? You think that is a proper and true definition of what not being a subset means, right?
please confirm.

ciao

- viole

 

[dybmh]

Your words.
are you moving away from them?

ciao

- viole

Asked and answered. It is a proper defintion, but that is not the defintion given in Chapter 1.

 

[dybmh]

nobody is making that assumption. A pretty silly claim, actually.

So, you stand by them? You think that is a proper and true definition of what not being a subset means, right?
please confirm.

ciao

- viole

Yes, they are, that is in chapter 2. That is how a material conditional , the technical name for the "implication" is defined. If you scroll back and look up the truth table you keep using, it is "Assume it's true..."

Since you haven't moved past chapter 1, you remain ignorant.

 

[viole]

Asked and answered. It is a proper defintion, but that is not the defintion given in Chapter 1.

I don’t care about chapters. forget the chapters.

i want to know whether that definition is your official definition that we can use to evaluate claims, from now on, at least for what concerns being a subset, or not being a subset.

in other words, are you ready to defend it or not?

don’t be afraid, I don’t bite

ciao

- viole