Deeper than primes

[dafydd]

You don't get the Unity, which is the source of any possible change, which is itself naturally unchanged, otherwise it can't be considered as the source of all changes.

Your awareness is floating upon the surface of changes, without being aware of the unchanged Unity that can't be known by believing in Unity.

Your examples are at the level of the naturally manifested and changed, where at this surface level belief is always involved simple because any given evidence is naturally changed.

By directly aware of Unity, no belief is involved anymore.

Wow,just wow.

 

[epix]

Yes, it's continuous, but it only takes values in the [-1,1] interval. Hence, not surjective from R to R, only from R to [-1,1]. This is not an opinion, this comes from the definition of surjectivity.

The term "R to R" refers to the type of numbers. R = real numbers, Q = rational numbers, N = natural numbers Z = integers, and so on. It got nothing to do with the size of an interval, such as [-1, 1]. If you look at the blue function, you see that it is injective from N to R. That means if the domain is a set of natural numbers and the co-domain is a set of real numbers, not all points in the co-domain get mapped. Here is a similar injection from N to Q.

Q......N
0 <-- 0
3/8
7/9
1 <-- 1
7/3
8/3
9/7
2 <-- 2

and so on.

The mapping between the members of set Apples and set Fruit is injective, coz A{apple}=F{apple} but A{apple}≠F{orange}.

Edit: Can you post the definition of surjectivity that you went by?

 

[laca]

The term "R to R" refers to the type of numbers. R = real numbers, Q = rational numbers, N = natural numbers Z = integers, and so on. It got nothing to do with the size of an interval, such as [-1, 1].

The term "R" refers to the set of real numbers. This is the standard notation used in mathematics.

You're wrong. I pointed it out. It's up to you to learn from it or not. I cannot help you further. In fact it's quite embarrassing, I just wanted to point out a small mistake, which would have been really easy to correct. Instead, you keep babbling on, for who knows what purpose. Suit yourself.

 

[epix]

You don't get the Unity, which is the source of any possible change, which is itself naturally unchanged, otherwise it can't be considered as the source of all changes.

Your awareness is floating upon the surface of changes, without being aware of the unchanged Unity that can't be known by believing in Unity.

Your examples are at the level of the naturally manifested and changed, where at this surface level belief is always involved simple because any given evidence is naturally changed.

By directly aware of Unity, no belief is involved anymore.

Hmm. You know, Doron, that you could be right? It really didn't occur to me that the cardinality of R is larger than the cardinality of the power set of the finite set of all characters that the mathematicians use to define a point. The consequence is that not all points on the R line segment can be covered. As a matter of fact, there are infinitely many points there that we can't define and therefore locate.

 

[epix]

The term "R" refers to the set of real numbers. This is the standard notation used in mathematics.

You're wrong. I pointed it out. It's up to you to learn from it or not. I cannot help you further. In fact it's quite embarrassing, I just wanted to point out a small mistake, which would have been really easy to correct. Instead, you keep babbling on, for who knows what purpose. Suit yourself.

You don't suppose I would consider stipulating the range of the co-domain to be [-1, 1] crucial to avoid a confusion. The graph was meant for Doron to see the periodicity of the red sine function as surjective function in comparison to the green, non-periodic bijective function.

Let me see the type of a sine function that satisfies your requirements and also mine, e.g. it would fit the graph so the periodicity could be seen. Don't embarrass yourself by not coming up with such function.

 

[epix]

The term "R" refers to the set of real numbers. This is the standard notation used in mathematics.

You're wrong. I pointed it out.

You pointed it out, but you didn't prove it.

Here is your statement: y=sin(x) is not surjective function from R to R.

If it is not, then by definition y=sin(x) must be injective function. That leads to a contradiction, coz no periodic function can be injective.

Math is not about "pointing things out"; math is about proofs, and as you see, your statement leads toward contradiction.

 

[laca]

You pointed it out, but you didn't prove it.

Here is your statement: y=sin(x) is not surjective function from R to R.

If it is not, then by definition y=sin(x) must be injective function. That leads to a contradiction, coz no periodic function can be injective.

Please, look up the definitions of injective and surjective functions. Your posts are becoming more and more full of fail. From the fact that a function is not surjective it does not follow that it is injective. A function can be any combination of the two, depending on its definition.

Math is not about "pointing things out"; math is about proofs, and as you see, your statement leads toward contradiction.

No, it doesn't. You, on the other hand, are becoming more and more silly. When I first replied I just assumed that you made a minor mistake when writing the post. Now I think you just don't know what you're talking about.

 

[epix]

Please, look up the definitions of injective and surjective functions. Your posts are becoming more and more full of fail. From the fact that a function is not surjective it does not follow that it is injective.

I didn't refer to "any function"; I clearly refered to function y=sin(x), coz you pointed to it. If this function is not surjective from R to R, then what type of function is it? The type of statements you've been using, such as "it ain't so" peppered with emotional outbursts is not enough of an argument. You still haven't PROVED that y=sin(x) is not surjective from R to R. The first step to do so is to identify the type of function which y=sin(x) is instead.

 

[laca]

I didn't refer to "any function"; I clearly refered to function y=sin(x), coz you pointed to it. If this function is not surjective from R to R, then what type of function is it?

It is neither surjective nor injective from R to R. This is basic stuff, which you would know if you had bothered to look up the definitions of injectivity and surjectivity.

The type of statements you've been using, such as "it ain't so" peppered with emotional outbursts is not enough of an argument. You still haven't PROVED that y=sin(x) is not surjective from R to R. The first step to do so is to identify the type of function which y=sin(x) is instead.

I proved it when I stated that it only takes values in the [-1,1] interval. I thought it is not necessary to spell it out, but here you go. Since R contains elements not in [-1,1], it follows that the function is not surjective. Since you seem to be exceptionally dense, I'll even provide a formal proof.

[latex]
Let $f:\mathbb{R}\rightarrow\mathbb{R}$, $f(x)=\sin(x)$. $f$ is surjective if and only if $\forall y\in\mathbb{R}$ $\exists x\in\mathbb{R}$ such that $f(x)=y$. Let $y=2$, $y\in\mathbb{R}$. We can see that $\nexists x\in\mathbb{R}$ such that $\sin(x)=2$, hence it is not surjective from $\mathbb{R}$ to $\mathbb{R}$.
[/latex]

Seriously, epix, this is basic stuff. It is beyond silly. Just stop it.

 

[epix]

It is neither surjective nor injective from R to R. This is basic stuff, which you would know if you had bothered to look up the definitions of injectivity and surjectivity.

That's right. Since I made the graph for Doron -- and he may go through this -- y=sin(x) is a "total" function (non surjective and non injective) from R to R, and the model mapping looks like this.
http://en.wikipedia.org/wiki/File:Total_function.svg

I proved it when I stated that it only takes values in the [-1,1] interval. I thought it is not necessary to spell it out, but here you go. Since R contains elements not in [-1,1], it follows that the function is not surjective.

You didn't prove it; you pointed out an inconsistency related to R --> R.
That's interesting. I made the graph to stress the mapping between various number sets, such as N to R and didn't bother with the ranges at all, thinking Doron wouldn't find out, but someone else did.

Since you seem to be exceptionally dense, I'll even provide a formal proof.

[latex]
Let $f:\mathbb{R}\rightarrow\mathbb{R}$, $f(x)=\sin(x)$. $f$ is surjective if and only if $\forall y\in\mathbb{R}$ $\exists x\in\mathbb{R}$ such that $f(x)=y$. Let $y=2$, $y\in\mathbb{R}$. We can see that $\nexists x\in\mathbb{R}$ such that $\sin(x)=2$, hence it is not surjective from $\mathbb{R}$ to $\mathbb{R}$.
[/latex]

Seriously, epix, this is basic stuff. It is beyond silly. Just stop it.

You just proved that sin(x) is not surjective from R --> R.

So y=sin(x) is non-injective and non surjective function from R to R, but is it surjective from R onto [-1,1]? I think it is not, coz every member of R/x-axis cannot map to every member of [-1,1]/y-axis, otherwise f(x) = x = sin(x). Double silly me . . .

 

[laca]

You just proved that sin(x) is not surjective from R --> R.

Which was kind of the point, but whatever...

So y=sin(x) is non-injective and non surjective function from R to R, but is it surjective from R onto [-1,1]? I think it is not, coz every member of R/x-axis cannot map to every member of [-1,1]/y-axis, otherwise f(x) = x = sin(x). Double silly me . . .

This is not even wrong, it's epix fail.

I've lost interest, to be honest. You seem to have no grasp of these basic concepts and to top it off, you seem to be unwilling and/or incapable of learning about them. I bow out.

 

[punshhh]

It is a located mark on an element which is non-local.

But the simple truth is that the dichotomy between the local and the non-local is an illusion exactly as the edge of a line segment (which is the local aspect) is actually inseparable of the line (which is the non-local aspect).

In other words, the truth is Unity, and Unity is manifested by at least the dichotomy between the local and the non-local.


In terms of Length, smallest is exactly 0 length, where any other length is defined relatively to it.

It gives the illusion that a point is the fundamental element, where the other lengths are define by elements with 0 length.

But as written above, Unity is really the fundamental truth beyond any dichotomy.


No, there is only a one point and by going beyond the illusion of the dichotomy between locality and non-locality, there is actually Unity, which is the one and only truth.


The inability of the local to completely cover the non-local provides the realm of infinite diversity, but the true realm is Unity.


No. Planck scale > 0.


Under the illusion of dichotomy there is the smallest element, called a point, which has exactly 0 length.


Under the illusion of dichotomy. there is an endless line with infinite length.


Under the illusion of dichotomy, Unity is perceived as Nothing.

Yes, I agree

 

[zooterkin]

Yes, I agree

You agree with nonsense?

 

[dafydd]

Yes, I agree

Agree with what?

 

[dafydd]

You agree with nonsense?

No surprise there. Perhaps our two maths experts can tell us what "Under the illusion of dichotomy, Unity is perceived as Nothing. " means. It sounds like pure babble from the sick bed. I love the way these guys string words together at random,I find it highly amusing. It only impresses others who have zero knowledge of the subject under discussion.

 

[epix]

Which was kind of the point, but whatever...



This is not even wrong, it's epix fail.

Can you prove it?

I've lost interest, to be honest. You seem to have no grasp of these basic concepts and to top it off, you seem to be unwilling and/or incapable of learning about them. I bow out.

You know that there is other proof, namely that sin(x) > |1| may not solve well. Like

x > arcsin|1|

returns a domain error. I found out about this like 150 years ago, even though you think that these basics were not present when I made the graph for Doron.

I thought that your proof would involve the Pythagorean Theorem and the unit circle showing all the reasons why sin(x)>|1| no worky. But I must appear much smarter to you, if you skipped the fundamental part of the proof. Thanks for the compliment.

 

[epix]

[latex]
Let $f:\mathbb{R}\rightarrow\mathbb{R}$, $f(x)=\sin(x)$. [/latex]

Seriously, epix, this is basic stuff. It is beyond silly. Just stop it.

That's funny, when someone makes a comment about the silliness of others and opens his argument with a term, which lacks the necessary rigor expected from someone who raises his finger to the stratosphere. You can't map from R --> R, coz domain and co-domain are two different concepts.

Here, learn the openers:

A function f: X → Y is surjective if and only if for every y in the codomain Y there is at least one x in the domain X such that f(x) = y.

I'm NOT saying that you are a counseling moron who happen not to have the slightest idea what he is talking about, coz your mistake is not a big deal at all within the context -- it doesn't obscure the meaning of your scribble.

So remember: surjective, from R to R and not from R to R, surjective. (See my graph.)

 

[punshhh]

It is a located mark on an element which is non-local.

But the simple truth is that the dichotomy between the local and the non-local is an illusion exactly as the edge of a line segment (which is the local aspect) is actually inseparable of the line (which is the non-local aspect).

Yes

In other words, the truth is Unity, and Unity is manifested by at least the dichotomy between the local and the non-local.

Yes, unity is unmanifest, for unity to become manifest (existent) it generates duality.
This duality is illusory, it cannot approximate the innate nature of unity as it is not a unity.

In terms of Length, smallest is exactly 0 length, where any other length is defined relatively to it.

It gives the illusion that a point is the fundamental element, where the other lengths are define by elements with 0 length.

Yes duality requires relativity to be existent

But as written above, Unity is really the fundamental truth beyond any dichotomy.

Yes Unity is the only explanation for existence, otherwise its turtles all the way down.

No, there is only a one point and by going beyond the illusion of the dichotomy between locality and non-locality, there is actually Unity, which is the one and only truth.

Yes I was visualising this one point, from the perspective of dichotomy, as
infinitely small/large. As a one point is not present in the duality.

The inability of the local to completely cover the non-local provides the realm of infinite diversity, but the true realm is Unity.

Yes I visualise this as the local manifesting as a mirror image or reflection of the unity. An infinite complexity representing through dichotomy the nature of the unity.

No. Planck scale > 0.

Yes, mathematics is only abstraction.

Under the illusion of dichotomy there is the smallest element, called a point, which has exactly 0 length.


Under the illusion of dichotomy. there is an endless line with infinite length.


Under the illusion of dichotomy, Unity is perceived as Nothing.

Yes the paradox of everything or nothing.

 

[dafydd]

Yes



Yes, unity is unmanifest, for unity to become manifest (existent) it generates duality.
This duality is illusory, it cannot approximate the innate nature of unity as it is not a unity.



Yes duality requires relativity to be existent



Yes Unity is the only explanation for existence, otherwise its turtles all the way down.




Yes I was visualising this one point, from the perspective of dichotomy, as
infinitely small/large. As a one point is not present in the duality.




Yes I visualise this as the local manifesting as a mirror image or reflection of the unity. An infinite complexity representing through dichotomy the nature of the unity.




Yes, mathematics is only abstraction.




Yes the paradox of everything or nothing.

More gibberish,devoid of any meaning whatsoever.

 

[The Man]

Yes



Yes, unity is unmanifest, for unity to become manifest (existent) it generates duality.
This duality is illusory, it cannot approximate the innate nature of unity as it is not a unity.

Ah the “unmanifest” unity that when ‘manifested’ becomes a duality which is an illusion because “it is not a unity”. I think you migth just need some better ‘manifestations’ or 'manafesting'.

You and Doron should get along handsomely.

Yes duality requires relativity to be existent

Would that be an actual duality or an illusionary duality and how would you tell them apart, relatively speaking? What if said existent duality was relatively unified, that is relative to other dualities?

Yes Unity is the only explanation for existence, otherwise its turtles all the way down.

So “Unity” “all the way down” is the “only explanation for existence”? Why? Because it is, well, ‘unified’ “all the way down”? Well, except for that whole manifest duality part, which fortunately is illusionary “as it is not a unity”. Are you sure there arn't some turtles in there somewhere too? Not even llusionary turtles that cannot approximate the innate nature of geese as they are not geese?

Yes I was visualising this one point, from the perspective of dichotomy, as
infinitely small/large. As a one point is not present in the duality.

At least one point is present in the duality of, well, two points.

Yes I visualise this as the local manifesting as a mirror image or reflection of the unity. An infinite complexity representing through dichotomy the nature of the unity.

Yep it sure sounds like you two have been reading the same fortune cookies or bubblegum cards.

Yes, mathematics is only abstraction.

As are a lot of concepts, like that “unity” you mentioned, though some abstract concepts are demonstrably more practical than others.

Yes the paradox of everything or nothing.

That’s not a paradox it’s a dichotomy and it seems a false one at that.