Cool discovery I discovered

[ALine]

X, being a set, and Y being a set.

X XNOR Y -> X XOR Y, is the basis of mathematics.

Mathematics, based on my research, is about relationships which can be described using functions. These functions relate or create new sets. However there is a problem. What actually IS a relationship.

Claim: A relationship is a symmetric difference -> symmetric addition.

Explanation: A symmetric addition is a similarity between two sets. It is a comparison between these two sets and everything else in the universal set. By comparing both obtain something neat.

Potentially a fractal. This is as far as I have gotten on the problem. 

[wtf]

6 hours ago, ALine said:

X XNOR Y -> X XOR Y, is the basis of mathematics.

The xnor logical connective is true if and only if X and Y have the same truth values. xor is true if and only if X and Y have different truth values. So far so good.

What does -> mean in this context? Is this a logical implication? That seems unlikely, since if X and Y have the same truth values, X xnor Y is true and X xor Y is false, resulting in a false material implication.

So, what do you mean by -> here?

 

 

6 hours ago, ALine said:

These functions relate or create new sets.

Mathematical functions never create news sets. Given two sets, there may be functions between them. But the sets have to already exist. Functions do relate them in terms of inputs and outputs, but this isn't a very meaningful way to put it.

 

6 hours ago, ALine said:

Claim: A relationship is a symmetric difference -> symmetric addition.

 

The symmetric difference of two sets is the set of elements that are members of one of the sets but not the other.

A web search on symmetric addition did not bring up any definition at all. What is symmetric addition. What is symmetric addition?

And as before, what does -> mean?

By relationship, do you mean relation? A relation between two sets X and Y is a subset of the Cartesian product of X and Y. That is, given two sets X and Y, a relation between them is a collection of pairs (x,y) that satisfy the relation. 

Is that what you mean by relationship? If not, what do you mean by relationship?

 

 

6 hours ago, ALine said:

A symmetric addition is a similarity between two sets. It is a comparison between these two sets and everything else in the universal set.

What is a similarity between two sets? Given two sets X and Y, how do I know if they are similar or not? What definition are you using?

Secondly, Russell showed in 1901 that there is no universal set. Are you working with some restricted universe of sets? Can you clarify what you mean by universal set?

 

6 hours ago, ALine said:

Potentially a fractal

What is potentially a fractal, and how so?

I believe you may have had some interesting personal insight about sets, but your exposition is unclear. I hope my questions can help you to better explain what you are saying.

Edited March 16, 2023 by wtf

[mathematic]

Looks like a lot of meaningless wordplay.

[ALine]

41 minutes ago, wtf said:

So, what do you mean by -> here?

I was using implication here.

41 minutes ago, wtf said:

Mathematical functions never create news sets. Given two sets, there may be functions between them. But the sets have to already exist. Functions do relate them in terms of inputs and outputs, but this isn't a very meaningful way to put it.

I may have been applying my sets of knowledge to a field of study which uses mathematics to make the above statement true.

44 minutes ago, wtf said:

symmetric addition

XOR Gate symmetric difference,

XNOR Gate symmetric addition, however I worded it wrong.

58 minutes ago, wtf said:

Secondly, Russell showed in 1901 that there is no universal set. Are you working with some restricted universe of sets? Can you clarify what you mean by universal set?

jesus math is old. Was not aware of this fact. Thanks for this.

58 minutes ago, wtf said:

Potentially a fractal

This was just banter more than stating any claims or facts.

Thanks for your responses.

This basis of the idea was that the implication emerged from the relationship.

[wtf]

12 minutes ago, ALine said:

I was using implication here.

But the implication is manifestly false, as I noted. If X and Y have the same truth value, then their xnor is true and their xor is false, resulting in a false material implication. Agree or disagree?

12 minutes ago, ALine said:

I may have been applying my sets of knowledge to a field of study which uses mathematics to make the above statement true.

Didn't understand this. Sets of knowledge? What do you mean?

12 minutes ago, ALine said:

jesus math is old. Was not aware of this fact. Thanks for this.

1901 old? The Pythagorean theorem is from 500BC and was known even before that. 

Edited March 16, 2023 by wtf

[ALine]

(relationship) [ X XOR Y -> X XNOR Y] (this was the first way I thought about doing it where XOR was the addition in mathematics because of the circle and the +, multiplication would be circle and x.

 

[wtf]

Just now, ALine said:

(relationship) [ X XOR Y -> X XNOR Y] (this was the first way I thought about doing it where XOR was the addition in mathematics because of the circle and the +, multiplication would be circle and x.

 

This is the opposite of the way you originally expressed it, and this implication is false as well.

Suppose X and Y have different truth values. Then X xor Y is true; and X xnor Y is false. True implies False is a false material implication. 

Your claim is false in both directions.

[studiot]

19 minutes ago, ALine said:

1 hour ago, wtf said:

Secondly, Russell showed in 1901 that there is no universal set. Are you working with some restricted universe of sets? Can you clarify what you mean by universal set?

jesus math is old. Was not aware of this fact. Thanks for this.

To be fair what he showed was "There is no set of all sets" ie no  Capo di Capo", no "One ring to rule them all.     

It is perfectly OK to posit a simpler universal set which is the complement of some set plus that set itself.       

 

I agree with the others that I saw no sense in your use of an arrow though.  

Nor do I understand your definition of a relation, which can be thought of as a partition of a set.                               

Edited March 16, 2023 by studiot

[ALine]

4 minutes ago, wtf said:

But the implication is manifestly false, as I noted. If X and Y have the same truth value, then their xnor is true and their xor is false, resulting in a false material implication. Agree or disagree?

Agree

4 minutes ago, wtf said:

Didn't understand this. Sets of knowledge? What do you mean?

Just expressing my limited amount of knowledge on the subject.

5 minutes ago, wtf said:

But the implication is manifestly false, as I noted. If X and Y have the same truth value, then their xnor is true and their xor is false, resulting in a false material implication. Agree or disagree?

Need some time to try and formalize this, have problems with this endeavor.

I admit defeat.

6 minutes ago, ALine said:

(relationship) [ X XOR Y -> X XNOR Y] (this was the first way I thought about doing it where XOR was the addition in mathematics because of the circle and the +, multiplication would be circle and x.

 

It being I have no idea how to formally explain it.

It being my idea/discovery.

Mathematics is the structuring of the universe, ergo nature, into a set of discoverable rules and formulations. These formulations are conceived by the human mind. A set is itself an inverse of reality due to those languages which better describe reality. Languages, of the romantic kind, describe humans endeavor to discern between the reality and fictitious efforts of noise. That's probably the best way I can put my discovery. I think I am trying to describe automata theory. Not sure though. Please help.

[studiot]

7 hours ago, ALine said:

Mathematics, based on my research, is about relationships

What do you mean by this ?

 

[ALine]

5 minutes ago, studiot said:

What do you mean by this ?

I mean to say that a relationship is the connection between two points in space in nature.

Also I mean a relationship is an object in math.

[studiot]

2 minutes ago, ALine said:

I mean to say that a relationship is the connection between two points in space in nature.

It is worth noting that there is some disparity in drawing the distinction between a relation and a function and considerable disparity in the notation employed.

So it is always wise to check the definitions and notations used in any particular work.

 

Here is simple explanation of how I like to think of relations

Given a set A we often like show that a 'relation' exists between certain pairs of the elements of A.
Such a relation can be expressed as a property statement that is true for some pairs of elements but false for other pairs.

A good notation that does not clash with other uses (such as the ~ symbols which may be reserved for a special type of relation) is

For all a, b in A

a R b denotes that b is related to a

c notR d denotes that d is not related to c

A relation property may take many forms.

For instance a is related to b if they have the same parity so all even numbers and all odd numbers are parity related.

(This is a relation that is not connected to a function)

Another relation that is not is function is the equation of a circle in a plane.

That is because there are two values of y for every value of x and functions are defined as being single valued.

This is the principle distinction between a function and a relation.

[ALine]

6 minutes ago, studiot said:

a R b denotes that b is related to a

Are relations the same as if conditional statements then? Or at the very least similar? Because with a if b, you have b -> a.

[studiot]

6 minutes ago, ALine said:

Are relations the same as if conditional statements then? Or at the very least similar? Because with a if b, you have b -> a.

No.

Does 4 implies 2 have any meaning?

Yet 4 is related to 2 and in this case 2 is related to 4 since they are both even.

Further this relation can be transferred so if 4 is related to 6 and 2 is related to 4 then 2 is related to 6.

The three statements

a R a     is called reflexive relation

a R b implies b R a is called symmetric relation

If a R b and b R c then implies a R c this is called a transitive relation.

 

Relations may satisfy none,  one or two or three of these conditions

If the last three are satisfied then the relation is called an equivalence relation and often given the symbol  a ~ b

Equality is an equivalence relation, but > is not since a > b  does not imply b > a.

[ALine]

52 minutes ago, studiot said:

Does 4 implies 2 have any meaning?

How do mathematicians define "meaning?" Because whenever I run into it I come to an existential road block.

But, yes I think I understand what you are saying in terms of Relations and my intuitive thought.

I think I got function and relation confused and did not understand each of there definitions are you have pointed out prior.

Random thought, could this be used to imply symmetry breaking in a field of study such as physics?

[studiot]

10 hours ago, ALine said:

How do mathematicians define "meaning?" Because whenever I run into it I come to an existential road block.

But, yes I think I understand what you are saying in terms of Relations and my intuitive thought.

I think I got function and relation confused and did not understand each of there definitions are you have pointed out prior.

Random thought, could this be used to imply symmetry breaking in a field of study such as physics?

Don't worry, meaning is not a defined mathematical term.
It is really a language/ philosophical thing which requires interpretation which in turn requires context.
Mathematics and logic, although different,  are about 'statements' and their consistency in the case of mathematics and validity in the case of logic, although there is obviously some overlap.

Would the statement "lines are green" add anything to the 5 axioms of Euclid ?

I haven't time at the moment, but I will try to address your other question later.

Edited March 17, 2023 by studiot

[ALine]

thank you

[joigus]

On 3/16/2023 at 4:24 PM, ALine said:

Potentially a fractal. This is as far as I have gotten on the problem. 

Sorry, a fractal what? From where?

[ALine]

was just spit balling @joigus

[joigus]

19 hours ago, ALine said:

was just spit balling @joigus

Oh, ok. I do that from time to time. Cheers!