/sci/ - Science & Math

>>9796991
It has highly conjectured that pi is an "normal number" (yeah virgin mathematicians literally named like that like wtf). every normal number has a property that you just mentioned.
but it does not represent the truth enough. not just only pi, but it has an 100% probability that an arbitrary real number has that same property.

>>9796991
>Liouville's Constant is an infinite, non-repeating transcendental number, but it follows the pattern of
>0.1100010000000000000000001...

How can it be infinite when it has a beginning? Infinity means no beginning and no end. If there is a beginning, there must be an end, logically impossible to have one without the other.

Mathematics has a flawed concept of infinity.

>>9797011
Mathematics defined infinity, and tetermined that "half of an infinity" and "quarter of infinity" and "one one billionth of an infinity" are all equal infinities.
Only when you get to Infinity Squared does it become something bigger.

Something that expands only "to the right" is equivalent to something that expands "both to the right and to the left" as points on each can be assigned to each other. It's the same situation as with "all natural numbers" and "all even numbers" being equal.

>>9796991
that cube isnt impossible

>>9797017
>Mathematics defined infinity
That's philosophy's job.
>and tetermined that "half of an infinity" and "quarter of infinity" and "one one billionth of an infinity" are all equal infinities.
>Only when you get to Infinity Squared does it become something bigger.

>Something that expands only "to the right" is equivalent to something that expands "both to the right and to the left" as points on each can be assigned to each other. It's the same situation as with "all natural numbers" and "all even numbers" being equal.
Assigning properties of finiteness to infinity is completely illogical, infinity cannot work that way.

>>9797020
That's the illusion dude

>>9797025
>That's philosophy's job.
fuck off.
Infinity is an incredibly useful mathematical concept, and has been defined within the field of mathematics in a certain consistent way.
If you want to argue math vs philosophy, you can say that we are actually discussing two completely different ideas, merely referenced by the same word. Just like mathematicians and botanist use the word "tree" to describe different ideas.

Maybe philosophical "infinity" is nebulous and indescribable. Fine.
Mathematics has a roughly similar concept that follows a whole lot of different rules.

>>9797011
>How can it be infinite when it has a beginning? Infinity means no beginning and no end.
proofs?

>>9797038
>Infinity is an incredibly useful mathematical concept
Did you just use the word "concept"? Concepts are in the domain of philosophy, not mathematics.
>If you want to argue math vs philosophy
That's not what I'm arguing for. Philosophy is not the nemesis of any intellectual pursuit, it's the exact opposite. Philosophy will give you a logically consistent framework of concepts that mathematics can use to advance itself. I believe that things like mathematics and science have been deliberately forced away from philosophy so that these topics stray further and further from truth, becoming increasingly complex and illogical.

>>9797048
It's based on fundamental, binary logic. Finiteness is the binary opposite to infinity. Finiteness requires a beginning and an end. Infinity must be the opposite to this, no beginning and no end.

>>9797050
Did you just use the word "concept"? the word "Concepts" are in the domain of linguistics, not philosophy.

>>9797061
the opposition of ~p & ~q is not p & q, but p or q.

>>9797061
Actually, concept is in the domain of engineering and design.

>>9797063
Please form a concept without using philosophy, only linguistics.

>>9797050
>these topics stray further and further from truth, becoming increasingly complex and illogical.
Mmmmh, do I smell an argument from common sense? Ah, just like mom used to make!

>>9797061
how is no end finite?

>>9797072
You're creating separation where there isn't one. Can you have an end without a beginning?

>>9797081
Please form a concept without using linguistic, only philosophy.

>>9797089
>>9797081
Guys, I'm a huge fan of the early 2000s italian power metal band "Concept" and I want you to please stop appropriating my culture

>>9797085
>how is no end finite?
Is there a beginning? Then there cannot be no end.

>>9797086
Please explain to me, in your logic.

>All Natural Numbers higher than 0 and lower than 10
>All Natural Numbers higher than 0
>All Natural numbers

Which of those sets are infinite?
For those sets thar are finite, please tell me how many members they have.

>>9797089
I can do this in my mind.

>>9797092
How inconsiderate of me, we need a safe space.

>>9797098
Sets by their very nature are not infinite because they have a beginning and an end.

The amount of members they have depend entirely on your definition of "natural number".

>>9797086
the death of the auteur. only end exists. they dont care about beginning, there's no beginning. just écriture makes the necessity of the end.

>>9797107
>only end exists.
That's like saying you can have 'up' without 'down'. Impossible, they necessitate each other.

>>9797105
How do you define a beginning and an end?
for "All Natural numbers" you will not encounter an end no matter which direction you go.

>>9797118
>for "All Natural numbers" you will not encounter an end no matter which direction you go.
Where's the beginning?

>>9797105
>The amount of members they have depend entirely on your definition of "natural number".
Ah, right, of course, because "natural number" is impossible to define. True, true. After all, numbers are a domain of philosophy, not mathematics. If only silly mathematicians stopped barging into matters that don't concern them, it would all be clear.

>>9797121
That's what I'm asking you. Is there one?

>>9797122
Is zero a "natural number"?
>>9797125
If you claim there is a set which contains all natural numbers, then this containment requires a beginning and an end. The word "all" implies a finite quantity. Perhaps set theory is wrong to assign such properties to things which do not have a beginning and end.

https://github.com/philipl/pifs

>>9797117
you should logically explain 3 gaps on that single thread :

> why is 'up' without 'down' impossible?
> what's the logic behind the proposition "'up' and 'down' necessitate each other"?
> consider all of them true. why the "up necessitate down" implicate "beginning necessitate end"?

>>9797138
> why is 'up' without 'down' impossible?
>what's the logic behind the proposition "'up' and 'down' necessitate each other"?
Because they are two sides of the same thing. How can you know what 'up' is without knowing what 'down' is? The binary must exist for it to make sense.
>consider all of them true. why the "up necessitate down" implicate "beginning necessitate end"?
As they are two sides of the same thing, just like hot and cold. You wouldn't know what hot is without knowing what cold is.

>>9796991
>Liouville's Constant
You seriously couldn't come up with a better example? Like 1.01001000100001000001...

>>9797095
proofs?

>>9797310
Do you have proof of a beginning?

>>9797026
This is a meme right? There's no 82 there.

>>9797315
what does that mean? how is beginning with no end finite?

>>9797325
I'm saying that a beginning with no end is impossible, either there is no beginning and no end, or there is a beginning and an end. Nothing else can work.

>>9796991
>reals

>>9797330
proofs?

>>9797011
>Infinity means no beginning and no end.

>>9797061
>doesn't understand De Morgan's laws
the absolute state of armchair philosophers

>>9797324
there is an 82.
It says you see an 82 if you have normal color vision. You do not

>>9797324
http://www.colour-blindness.com/colour-blindness-tests/ishihara-colour-test-plates/

Bullshit I passed all of these. I just can't see that one.

>>9797348
http://www.colour-blindness.com/colour-blindness-tests/ishihara-colour-test-plates/

Bullshit I passed all of these I just don't
see that one

>>9797061
finite: Has beginning and has an end.
infinite: Has no beginning or no end.
What is hard to understand about this?
>>9797086
example of beginning with out end: A ray
example of end without beginning: A ray

>>9797359
>>9797361
Are you worried? Plenty of color blind people lead fulfilling lives, you're gonna be okay.

>>9797361
Be grateful some people can't see.
They make settings for colorblind people in games and shit

>>9797370
I know that I'm not color blind because my brother is and I can see tons of stuff that he can't.

>>9797359
So this is what a low IQ poster looks like

>>9797374
>he doesn't know

>>9797338
This is self-evident logic.
>>9797340
Explain how that's wrong?
>>9797346
What's the difference between the concept of finite and the concept of infinity?

>>9797381
Supposing your statement is true and a finite object has both beginning and end. And lets also suppose that infinity is the binary opposite of the finite, like you said.
So now we have two conditions for an object to be finite:
1. It has a beginning
2. It has an end.
Now both these conditions need to be satisfied for an object to be finite. Therefore, if an object fails to satisfy one (or both) of these conditions, it is infinite. Therefore an infinite object must be, by your definition, an object that has no beginning OR no end (or both). I really shouldn't have to explain this to you. Look up De Morgan's laws for a more formal explanation.

>>9797381
so no proofs eh? that's what i thought you're just one of them cocksuckers

>>9797381
Sorry, I forgot to refute your other point. Sure, since the difference between an "end" and a "beginning" is rather arbitrary, it's hard to say that an object can hypothetically only fulfill one of those conditions.
However, lets take a more sane definition and just say an object ought to be finite in all directions to be finite entirely. This removes the ambiguity of beginning and end. This also lets a ray be considered an infinite object, as it is a line which extends infinitely in one direction.

>>9797368
>example of beginning with out end: A ray
>example of end without beginning: A ray
This is my contention. It cannot be finite on one "end" and infinite on the other, this is nothing more than an illogical metaphysical concept.

>>9797011
by allah not in this thread you don't

>>9797399
You could make that distinction and consider the object to be partially infinite (or partially finite), but I don't see that as being a very useful definition. You should be considering infinite to be a synonym for unbounded, and a ray is certainly unbounded. By definition, it extends in one direction in an unbounded way, it is infinite.
And please also be aware that you can both find infinity to be logically incoherent and accept the mathematical definition of infinity. This is a different concept than what you're probably considering infinite, they just unfortunately share the same word. It is certainly possible to consistently reason about objects without bounds within the framework of standard mathematics, without concern for whether these objects can exist in nature. Please stop conflating philosophical infinity with a well-defined mathematical concept.

>>9797388
>Therefore, if an object fails to satisfy one (or both) of these conditions, it is infinite. Therefore an infinite object must be, by your definition, an object that has no beginning OR no end (or both).
No, if an object has a beginning, then it must also have an end. If something has no beginning, then it must not have an end. "Beginning" and "end" are two sides of the same thing, they cannot be separated.
>>9797392
I'm a philosopher, not a mathematician. It's your job to come up with the proofs, all I know is the logic is sound.
>>9797395
>an object ought to be finite in all directions to be finite entirely. This removes the ambiguity of beginning and end. This also lets a ray be considered an infinite object, as it is a line which extends infinitely in one direction.
With that definition, you would have to say that for something to be infinite, it must infinite in all directions, which a ray is not.

>>9797408
I'm sorry, but you really seem to be thinking of some different form of infinity than I am. I can concede that your definition of infinity does not allow for a ray to be included. I take infinity to mean something is unbounded, this is the standard mathematical definition. If you're truly a philosopher you must know that it's pointless to argue about something when you can't even agree on the definitions. Also any good philosopher ought to know some first order logic, the professor I learned philosophy from certainly was proficient.

>>9797402
Sorry Allah.
>>9797406
>>9797410
I understand that the concept of an unbounded ray can exist within a mathematical framework, however my problem with this is that it is not logically sound concept that should be used within mathematics. Just because it can be created, doesn't mean it should be used. Mathematics should reflect observable reality as much as possible, that's where its power lies.

>>9797415
>it is not logically sound concept
Show me a proof that is incorrect because it uses the mathematical concept of infinity.

>>9797415
I disagree with your idea of mathematics needing to reflect reality. That's the job of physics. Physics is basically math but restricted to reality. I find it strange that a philosopher would not have an appreciation for the abstract. Also do note that if we restricted ourselves to things that only existed in physical reality then a lot of very useful mathematics would never have been discovered. Often these abstract concepts can be applied in surprising and useful ways, as infinite concepts have demonstrated many times. Mathematics is merely the study of what conclusions we can draw from certain axioms, it's important that we study all the logical consequences because the useful concepts can come from surprising places; if some of it seems like naval gazing nonsense that's just a consequence of mathematicians' thoroughness.

>>9797421
https://en.wikipedia.org/wiki/Banach–Tarski_paradox

>>9797421
That's not the argument, you can use mathematics to prove an infinite amount of useless things.
>>9797423
>Often these abstract concepts can be applied in surprising and useful ways, as infinite concepts have demonstrated many times.
Abstract concepts must follow formal logic if they are to be used in reality. Show me how the mathematical concept of infinity has been used practically in reality?

>>9797408
A ray may indeed be bounded or infinite, but simply stating either doesn't make any case.

Suppose another case where a line is defined to extend forever in both directions. This type of infinity seems to suit your definitions. Now, we look at any point on this line and define a ray going to the right and ending wherever the line ends in that direction. What is the length of the ray?

>>9797435
>must follow formal logic
anon, you don't even understand de morgan's law, you can't possibly be lecturing the mathematicians on logic.

>>9797440
>Suppose another case where a line is defined to extend forever in both directions.
Don't you mean all directions? Again, a "line" is a finite concept, it can never be infinite, otherwise it would not be a line in the first place.

>>9797455
>a line is a finite concept
wrong, you're thinking of a line segment
a line is literally by definition infinite

>>9797435
>it is not logically sound concept that should be used within mathematics
>That's not the argument, you can use mathematics to prove an infinite amount of useless things.
wtf is your problem
you said it's not logically sound for mathematics I ask where the problem is and you say that's not an argument and insult math.
>>9797433
https://en.wikipedia.org/wiki/Axiom_of_choice

>>9797455
Okay, literal friend.
Using the real number line, how many numbers are between 0 and 1?

>>9797449
>de morgan's law
De Morgan's Law would consider "beginning" as being a separate set to "end", when they are not separate at all.

>>9797458
>a line is literally by definition infinite
Infinite width?

>>9797466
>you said it's not logically sound for mathematics I ask where the problem is and you say that's not an argument and insult math.
Mathematics should be using logically sound concepts. If you don't have this fundamental grounding in formal logic then you are essentially a blind man navigating in a meta-logical playground that leads nowhere other than ever increasing complexity.

>>9797467
>Using the real number line, how many numbers are between 0 and 1?
Zero isn't a number so it cannot be used as a beginning for other numbers to be between.

>>9797483
Boring troll is boring.

>>9797510
What property(s) does zero have that classifies it as a "number"?

>>9797577
Anyone going to answer this?

>>9797577
Well it can describe a quantity of objects. If someone asks how many apples you have, you can say 1 or zero.

>>9797634
Zero isn't a quantity, it's the lack of quantity. It's exactly the same as saying you have no quantity of apples.

>>9797647
Would you say that the first number is one?

>>9797654
I'd say the only real number is 'one' and all other numbers are just different ways of expressing different quantities of this base expression of quantity.

>>9797672
Im guessing you think our universe has a beginning? And therefore our space and time? If so, I’d like to know your opinion on what the boundary of space or the end of time may be like.

>>9797361
Most of the color vision test don't capture all variants of color blindness. Passing those doesn't mean that you have normal color vision, just that you don't specifically have some of the more common kinds of color-blindness. There's clearly an 82 there.

>>9797687
Yeah it’s obviously one of the “harder” tests because it’s not as prominent at first glance, but I still see it. I wish I knew what the different variants were and the statistics for these traits among populations.

>>9797681
>Im guessing you think our universe has a beginning?
Nope, because this implies that the universe came from "nothing", which is logically absurd, or the universe has an infinite chain of "beginnings" ruled by determinism, which is just circular logic and doesn't explain anything.

test

>>9797478
Define mathematics

>>9797690
>>9797687
Ok smart aleck, how about you edit the picture to point out where the 82 is?

>>9797470
No, length.

>>9797011
Learn about ordinals.

>>9797714
Nothing is truly infinite and has no limits. If it were unable to create, it would be defined by the ability to not create, and would therefore be limited, and therefore something, a contradiction.

Not only that, but Nothing is the most necessary “first” state because it needs no cause. It’s “existence” isn’t arbitrary but understood as being necessary. And since the inability to create is impossible, something would be possible.However, Nothing is never forced to create or not to create; it is where indeterminism truly lies. Only the Void has free will.

As another proof, consider the relation between cause and effect. For change to occur, the potential must be distinct from actual. But if all existence is actual, then the potential must be non-existence, or nothing. Something and Nothing are also distinct in that Nothing is infinite, infeterministic, and necessary, while something is the opposite of each.

>>9796991
>Infinite possibilities != all possibilities, after all.

>>9797011
>Mathematics' concept of infinity.
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

>>9797072
~p & ~q / p & q / p | q
https://programming.dojo.net.nz/study/truth-table-generator/index

>>9797745
It doesn't have a quantifiable length if it's infinite. Something can't be infinitely long, length requires the property of finiteness to make sense. Calling something infinitely long is like saying that it doesn't have a length, because it moves out of the realm of measurement.
>>9797748
No.
>>9797751
>Nothing is truly infinite and has no limits. If it were unable to create, it would be defined by the ability to not create, and would therefore be limited, and therefore something, a contradiction.
The problem with using the word "nothing" is that you're using something (a word) to describe something that lacks any description and it isn't a thing that exists, by its very nature.

>Not only that, but Nothing is the most necessary “first” state because it needs no cause.
"Nothing" cannot be a state of anything, because a "first state" is something.
>Only the Void has free will.
The void can't have anything.
>Something and Nothing are also distinct in that Nothing is infinite, infeterministic, and necessary, while something is the opposite of each.
"Nothing" cannot "be" infinite, for that would be something.

>>9797789
>mystic bs
>>>/x/

>>9797789
I don’t know how else to describe Nothing but as a “state” of non-existence. You still know what I mean, unless you think it’s impossible for there not to be Something. And when I say Nothing is infinite, I mean that it is not finite. It has no infinite quantities such as infinite space and such, but it has no limits, and therefore isn’t finite.
>the Void has free will
This was more of a jab at those who believe humans have free will. Obviously the void has no will, but it is free from constraints and is essentially random in its creation.

>>9797714
>>9797751
>>9797789
Also, the claim that something from nothing is absurd would only apply in our universe. Within our system of rules, it would be surprising to see objects pop into existence when we’ve never experienced it before and believe in causality. But Nothing is not within a system that adheres to logical rules and causality; you’re applying this system’s rules to the thing that created the system. This implies that the system has always existed, for its rules have always existed, when its rules are in fact entirely contingent and only logical because we judge them to be.

Btw, what is the alternative to believing something came from nothing? I want to hear your reasoning for your claim.

>>9797806
>I don’t know how else to describe Nothing but as a “state” of non-existence.
It's impossible to describe because there's nothing to describe.
>And when I say Nothing is infinite, I mean that it is not finite.
"Nothing" isn't finite or infinite, it cannot have the property of limits or no limits, it simply does not exist.
>This was more of a jab at those who believe humans have free will. Obviously the void has no will, but it is free from constraints and is essentially random in its creation.
How nice of your non-conscious, non-freewill having processes to tell you that you don't have freewill.

>>9797478
>argues about formal logic but doesn't understand that ~(p ^ q) =/= ~p ^ ~q

>>9797361
being this insecure :DD

>>9797374
there are many different kinds

>>9797026
nice merchant

>Scrounge /sci/ for the only math related thread
>it's literally 100 posts explaining to some retard what the definition of infinity is
I'm getting my PhD in math soon. Why the hell do I still come here?

>>9797026
doubting brainlets don't know how to open this up in photoshop to check the RGB values. many such cases

>>9798840
You're right, even a brainlet like you knew!

>>9797061
Are you literally retarded?

>>9797324
Yes, there is no 82

>>9797406
> partially infinite
This is a troll trying to derail an interesting convo

>>9797338
m-muh feelings

>>9797020
>>9797324
Found the autist.

>>9797408
>With that definition, you would have to say that for something to be infinite, it must infinite in all directions
HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA
Dude, just go back to /lit/.

>>9796991
Even itself cannot whole fit whitin itself./

>>9797006
Kys engicuck

>>9797100
>I can do this in my mind.
No you cant, in a similar fashion to you cant visualize 4 space dimensions. More on point you are an idiot arguing from your common sense against a defined and useful framework.
Neck yourself

>>9800217
>you cant visualize 4 space dimensions
Speak for yourself.

>>9797081
>t. Autissimus maximus

>>9797017

The two "cubes" don't have the same size

How is that an optical illusion?

>>9802640
That's the joke
All of OPs pics are like that

>>9797764
That part is correct, retard

>>9797017
pretty sure infinity squared is still the same thing

>>9802640
https://www.youtube.com/watch?v=rAbNyJNvKCA

>>9803964
it's not. then the list of all the integers would be as big as the list of all the real numbers.

>>9796991
If pi contains every permutation of numbers, then it contains Liouville's Constant. If Pi contains Liouville's constant, then it does not contain every permutation of numbers.

>>9804436
First of all, infinity squared is undefined in almost any version of the extended reals. If we abuse notation, then taking two to the power of any infinite cardinality yields a strictly bigger cardinality, corresponding to taking the power set of a set of some cardinality. The set of all natural numbers is in bijection with the set of all squares. The set of all squares is countably infinite, and under this analogy there are therefore countably infinite squared natural numbers. But there are countably infinite natural numbers, so countably infinite squared "equals" countably infinite.

>>9797647
no its not. its the quantity which is the predecessor of 1 and successor of -1.

"no quantity" is when a quantity isn't applicable to a given concept.

>>9797017
If 6oure talking about infinity as a set, then Countable infinity squared = countable infinity, pic related. If you're talking about infinity as a number then you're retarded.

>>9797577
Its inclusion in the sets of whole numbers, rational numbers, real numbers and complex numbers is necessary to give them a decent algebraic structure.

>>9797011
It starts with infinite zeros before the decimal point, which were omitted here, but feel free to write down the complete number whenever you feel like it

>>9797038
there are many types of infinity