/sci/ - Science & Math

[Anonymous No.15043504]

/sci/ BTFO'd once again by the best programmer alive

[Anonymous No.15043512]

>>15043504
>geohotz actually browses /sci/
whoa...

[Anonymous No.15043513]

>Worthless nobody's CS midwit opinion on mathematics

Woah

[Anonymous No.15043521]

>>15043513
>bro, it's just the only branch of maths that has actually to do with tangible reality of converting my schizo abstractions into results!
yeah, who cares right? when I want to actually know the value of an integral I'm sure my computer performs a super taks of infinite processing power!

[Anonymous No.15043522]

>>15043513
Math is not real, maybe in a mathematicans delusions. Computers know better, you can calculate only with finite things. As your brain too has finite things i.e. neurons, real numbers literally dont exist.

[Anonymous No.15043543]

>>15043522
Calculation is an application of math. You have things twisted

[Anonymous No.15043545]

>>15043504
oh no.. he's retarded

[Anonymous No.15043553]

>>15043543
>electrons passing through silicon is an application of set theory
the absolute state of the cult of calculus

[Anonymous No.15043555]

>>15043543
You seem to assume math is something abstract like heaven skydaddy. Math is actually solid and everything abstract is just schizo and do not exist.

[Anonymous No.15043562]

>>15043521
>it's just the only branch of maths that has actually to do with tangible reality
Get a grip. The only reason we've kept math around for thousands of years is because it is useful.

[Anonymous No.15043570]

>>15043555
But 95% of math is abstract like heaven skydaddy

[Anonymous No.15043587]

>>15043504
I'd attest that code quality would improve if programmers started on Wildberger, we take too much for granted in the not-so-real real number system

[Anonymous No.15043598]

>>15043504
>claims to be a finitist
>speaks of cardinality as if it's a concept applicable to the integers

[Anonymous No.15043599]

Math doesn't aim to be "real" it just aims to be consistent. Provided it is, it can be applied by others in both real and hypothetical scenarios, this is not the work of the mathematician.

[Anonymous No.15043600]

>>15043570
95% of math is a mathematical circlejerk not useful IRL

[Anonymous No.15043604]

>>15043599
You can be consistently gay by not having sex with women. Useful? Only if you believe in the globohomo agenda

[Anonymous No.15043614]

>>15043604
>globohomo
>gay
>sex
>in a thread about cardinality and finitism
You think you're witty and funny but you're just a retard that need to take some time off this site, unironically go outside and touch grass.

[Anonymous No.15043680]

>>15043513
Honestly, why are csfags like that? I have yet to meet one that isn't incredibly cocky. It's not just math and other sciences that they give their unneeded opinion on but there's also this phenomenon of young (especially Silicon Valley) programmers going on far too dangerous hikes and dying.

[Anonymous No.15043690]

If infinite sequences don't exist then that means sqrt(2) can be expressed as a fraction.

[Anonymous No.15043697]

Why are CS fags so insufferable?

[Anonymous No.15043732]

kek i knew this would be posted here

[Anonymous No.15043773]

>>15043614
You claimed consistency is a measure of mathematics, i gave you an example of it and you couldnt have counter arguments. I won, modern math is abstract, religious circlejerk, not bound in reality rules

[Anonymous No.15043783]

>>15043521
>computers can't do it therefore its not useful

[Anonymous No.15043784]

>>15043555
>You seem to assume math is something abstract
Yes.

[Anonymous No.15043786]

>>15043783
then please provide 1 useful mathematical finding that cannot be computed

[Anonymous No.15043787]

I'm being pedantic here, but it bothers me when people write "BTFO'd". BTFO already stands for " blown the fuck out", so what's the extra D for?

[Anonymous No.15043791]

>>15043787
for the same reason people say "lmaoing", the acronym becomes a verb and you're not supposed to mentally expand it when reading

[Anonymous No.15043824]

>>15043784
Then it can be anything. Let there be least upper bound is a religious statement. Let there be light, is quite much same, but at we least know there is light we see it with our eyes

[Anonymous No.15043827]

>>15043787
BloweD the fuck out

[Anonymous No.15043930]

>>15043827
haha, bee'd tee eff oh

[Anonymous No.15044116]

If there are no infinite sequence, surely every sequence has a last, final element. Then what is the last element of the sequence [math]a_n = n + 1[/math]? Can any finitist on here tell me this number that they assert exists?

[Anonymous No.15044131]

>>15043504
BASED

[Anonymous No.15044136]

>>15043787
In much the same way SPQR stands for Senatus Populusque Romanus.

[Anonymous No.15044137]

>>15043598
>>speaks of cardinality as if it's a concept applicable to the integers
Cardinality of finite sets is just counting the number of elements. Second, the integers can actually be said to exist to some extinct. The real numbers or any of these "uncountable infinite sets" can't really be said to exist by any logically honest person.

[Anonymous No.15044139]

>>15044137
name one logical argument for the nonexistence for the real numbers

[Anonymous No.15044140]

>>15043787
It's more naturally to attach 'd to the end to indicate past tense where as BTFO is often used in future or present tense.

[Anonymous No.15044144]

>>15044116
The last element of the sequence is the last one you can physically write down in decimal form.

[Anonymous No.15044148]

>>15044144
Why can't I use base 2 or assign a symbol to this number and continue adding 1 to it? Do you actually have any argument?

[Anonymous No.15044156]

>>15044139
I've never seen a real number and neither have you. I've never seen a proper definition for a real number and never have you. The only thing there is happens to be just circular reasoning. You want to believe there's such thing as a real number, so you either make up a system of convenient assumptions (these aren't even proper first principles or even proper definitions) to try to prop up the idea, or, you imagine that there is a real number somehow at the end of some "infinite sequence" and since you can't find it, you claim the sequence itself is the real number or even worse and then you fall back onto the first case. So there are no coherent arguments for the existence of a real number. Therefore it is reasonable to maintain the default hypothesis, that "real" numbers don't exist in any meaningful fashion.

[Anonymous No.15044165]

>>15044156
>I've never seen a real number and neither have you
[math]\sqrt{2}[/math]
>I've never seen a proper definition for a real number
A real number is an element in the set of real numbers.
>Therefore it is reasonable to maintain the default hypothesis
What the fuck is a "default hypothesis"? If you can't prove that something doesn't exist, that means that whether it exists or not is an open question.
In the case of real numbers, it's not difficult to construct them using rationals or some other fields, so your claim is clearly false.

[Anonymous No.15044174]

>>15044148
>assign a symbol to this number and continue adding 1
Imagine if you were in a test where someone wanted you to calculate
[math] (10 \Delta 2 + 23^5 - 15)(842) [/math] and you just said "we'll name the name the number [math] \alpha [/math]" and move on. Can you or I say you calculated the indicated number? Absolutely not. If supposing you claimed to have a number "N" yet you cannot physically write it down, store it on a computer, etc. you really are claiming something that can be considered false. If you're saying N is given by some arithmetic expression yet you cannot physically resolve the expression, then you really cannot claim the number exists. If then you try to avoid responsibility by claiming "this symbol represents this 'number,'" or say something like "I'm going to calculate N in base N," you're doing nothing but ignoring the proper criticism. A simple criteria, If you cannot calculate a number, it doesn't exist.

[Anonymous No.15044192]

>>15044174
>Absolutely not.
Why?
You don't actually say why not, you are just claiming it out of intuition. If we define [math]\alpha[/math] as the number resulting from these functions, then it is clearly by definition this number.
>cannot physically resolve the expression
How do you physically resolve any expression? By stacking cans in a grocery store?
>If then you try to avoid responsibility by claiming "this symbol represents this 'number,'"
Do you deny the existence of numbers 1,2,3,...,9 because we define them to be represented by these Arabic symbols? Or are those symbols somehow different from [math]\alpha[/math]?

[Anonymous No.15044199]

>>15044165
I've never seen this alleged [math] \sqrt{2} [/math] and neither have you. Moreover, there is no reason to pretend such a thing exists. If you want to define a rational valued matrix algebra like the one given in terms of [math] \begin{pmatrix} 1 & 0 \\0 & 1\end{pmatrix}, \quad \begin{bmatrix} 0 & 2\\ 1 & 0 \end{bmatrix} [/math] and then call the matrix [math]\begin{bmatrix} 0 & 2\\ 1 & 0 \end{bmatrix} [/math] the square root of 2 feel free to do so. But there is no such thing as "number" which satisfies [math] x^2 = 2 [/math] in the same sense of an integer or rational number people imply when referring to the "real" numbers.
>A real number is an element in the set of real numbers.
Define set. Define element. Provide a definition of real number that depends entirely on the natural numbers, integers, and rational numbers and their arithmetic without any dubious assumptions like those from the "axioms" of set theory.
>What the fuck is a "default hypothesis"?
>If you can't prove that something doesn't exist
The default hypothesis is to assume a claim is false if cannot be proven true.
>In the case of real numbers, it's not difficult to construct them using rationals or some other fields, so your claim is clearly false.
There is not a person who calculated the real numbers in a coherent or reasonable fashion.

[Anonymous No.15044207]

>>15044199
Define calculated. Define arithmetic. Define integer. Define number.

[Anonymous No.15044214]

>>15044137
Yes, as a finitist you can say that the integers exist. But the collection of ALL integers is problematic.
You can speak of "the integers" in an informal way, but you can't treat/manipulate "the integers" as a formal mathematical object.

Cardinality is a property of sets.
Talking about the cardinality of the integers implies that "the integers" is a set, which classical finitists would disagree with.

For a finitist, "The cardinality of the integers" is as nonsensical as "the mass of sourness".
Mass is a property of physical objects, not flavours.

[Anonymous No.15044215]

>>15044192
>Why?
>You don't actually say why not, you are just claiming it out of intuition. If we define α as the number resulting from these functions, then it is clearly by definition this number.
I already debunked this in the post you're responding to. If you cannot write down a number in terms of a generic base, then you cannot claim to have written down anything related to a number.
>How do you physically resolve any expression? By stacking cans in a grocery store?
By performing all the operations indicated in the expression to find the number. I.e. 2*(2 + 3) = 2*5 =10.
>Do you deny the existence of numbers 1,2,3,...,9 because we define them to be represented by these Arabic symbols?
Except 1, ..., 9 can be represented in any base without having to invent new symbols for them and you can actually compute them in all other bases without resorting to inventing new symbols to pretend you calculated a number.

[Anonymous No.15044226]

>fake things like infinite sequences

int i = 0;
while (true) { print("%d\n", i++); }

[Anonymous No.15044229]

>>15043787
>what's the extra D for?
it's for your mom

[Anonymous No.15044237]

>>15044207
>Define calculated. Define arithmetic. Define integer. Define number.
You're just being unreasonably obtuse at this point. You lost on logical grounds so you resort to this ill-conceived attempt to enforce your fantasy. "Number" as in "natural numbers" and the standard arithmetic on them (just an extension of the primitive activity of counting) are the only true undefined objects and the only true axioms of mathematics. Calculation is just counting. Arithmetic and Natural numbers are just fundamental aspects of being a human being. "Sets," "Classes," "Elements," etc. and the convenient shoehorned assumptions mislabeled "axioms" outside of the very restrict finite cases, are all ill-defined dubious notions that lead to a variety of paradoxes alongside the logical fallacies used along with them.

[Anonymous No.15044240]

>>15044214
>For a finitist, "The cardinality of the integers" is as nonsensical as "the mass of sourness".
I have to agree with that.

[Anonymous No.15044248]

>>15044215
>2*(2 + 3) = 2*5 =10
As you can see by the equal sign, the number 2*5 is equal to 10. There's no difference between writing down 2*5 and 10 (otherwise they would be inequal).
>Except 1, ..., 9 can be represented in any base without having to invent new symbols for them and you can actually compute them in all other bases
This is not true for irrational number bases, where integers are infinite sequences but irrational numbers are finite sequences.

[Anonymous No.15044264]

>>15044248
>There's no difference between writing down 2*5 and 10 (otherwise they would be inequal).
There is a difference. The left-hand side is an arithmetic expression, that is a collection of two or more numbers and arithmetic operations between them. The right hand side is a number. The equal sign, an admitted overused symbol with many meanings, in this case means "evaluates to" as in "after you finish performing the arithmetic operations, you find the number ___"
>This is not true for irrational number bases
There is no such thing as an "irrational number"
>where integers are infinite sequences but irrational numbers are finite sequences.
This is just a silly word salad at this point and you're making yourself less intelligent by playing this silly game.

[Anonymous No.15044306]

>>15044264
>The left-hand side is an arithmetic expression, that is a collection of two or more numbers and arithmetic operations between them. The right hand side is a number.
No, both sides are a written sequence of symbols.
What is supposed to be an "arithmetic expression"? The decimal base is defined in terms of addition and multiplication, so the other side of the equation means exactly [math]1 \cdot 10^1 + 0 \cdot 10^0[/math]. I don't see the difference between this notation and the notation 2*5.
I think you're confusing symbols (the Arabic numerals) with numbers, which is an elementary mistake.
>This is just a silly word salad at this point and you're making yourself less intelligent by playing this silly game.
Are these words too hard to understand for you?

[Anonymous No.15044363]

>>15044306
>No, both sides are a written sequence of symbols.
The depth of your retardation is even worse that I realized. Enjoy think this retarded non-argument means anything.
>What is supposed to be an "arithmetic expression"? The decimal base is defined in terms of addition and multiplication.
>so the other side of the equation means exactly [math] 1⋅10^1+0⋅10^0[/math]
Ah yes, a common mistake. Defining 10 in terms of itself. You should've learned it's bad form to do so.
>Are these words too hard to understand for you?
You're not as smart as you think you are.

[Anonymous No.15044406]

>>15044363
And of course the mathlet is a subzero iq ESL. You will never be a mathematician, Ivan.
>Ah yes, a common mistake. Defining 10 in terms of itself. You should've learned it's bad form to do so
You can use base 2 to define base 10 if you think that.
[math]10 = 1 \cdot 1010^1 + 0 \cdot 1010^0[/math]. Looks quite similar, but the left side is the symbol "10" in decimal and on the right side is a sequence of symbols that uses the binary base.
A different way to define "10" in a field may be to define it as the sum of 10 1's, i.e. 1 + 1 + 1... but of course you cannot define fractions using this notation since that requires taking the inverse of something.

[Anonymous No.15044928]

>>15043786
No point in arguing with you since you'll just claim the finding is "not useful".

[Anonymous No.15044933]

>>15044199
>Define set. Define element.
They can be left undefined primitives, brainlet. The ZFC axioms were made for this exact reason. In fact, they are essentially defined by them. Here's a definition: They are the "things" which fulfill the ZFC axioms.
>>15044237
>mislabeled "axioms"
Not a mislabeling, brainlet.
>all ill-defined dubious notions
See the ZFC axioms.
>lead to a variety of paradoxes alongside logical fallacies
Which?

[Anonymous No.15044937]

>>15043773
>>15043604

[Anonymous No.15044940]

>>15043783
This but unironically.

[Anonymous No.15044959]

>>15043600
>>15043555
>>15043824
>brainlet who can't into abstraction
LMAO
>"Let there be" is a religious statement
"Let" is an imperative, son. In mathematical logic, it's a statement to which the condition that it is true is added (not the belief in that statement by the author). By demonstrating that this assumption leads to no contradiction and its negation would, its truth-value is justified. It's NEVER necessarily apodictically true, you fucking retard.
The vast majority of mathematicians aren't platonists either, moron. They're formalists, which is the thing between platonism and your just-as-religious finitism.

[Anonymous No.15044983]

>>15043504
snails have gone extinct

[Anonymous No.15045001]

>>15044959
So, gay? You are a hand waving faggot, never a scientist

[Anonymous No.15045008]

>>15043690
What is sqrt(2)? Define it.

[Anonymous No.15045015]

1. Let there be God, thy Lord
2. Let there be no other gods, but thy Lord

With these Axioms, it is consistent God is most powerful being existing. The second condition denies existence of other godlike beings, thus it is Consistent, God thy Lord, is the sole most powerful Existence in universe. The first Axiom Quarantees He be existing.

[Anonymous No.15045022]

>>15043504
>programmer
Because Infinity immediately breaks his entire field, no shit dumbass!

[Anonymous No.15045024]

>>15045008
Square Root of Two is square root of two. Axiom: Let there be least Number , whose square is equal or over Two. With this axiom it must be existing as I said it LET BE

[Anonymous No.15045030]

>>15045022
Infinity has well defined bit sequence :) you mad mathfag? Like your brain gives infinite a finite reservation of brain cells, so do computer give it finite bits.

This is consistent.

[Anonymous No.15045096]

>>15045024
Two doesnt have a square root, as euclid proved.

[Anonymous No.15045097]

>>15044933
Why do you believe in these axioms?

[Anonymous No.15045121]

>>15045097
because through the millennia we have developed maths that works.
ZFC axioms are a very simple and mostly intuitive way of basing what we have developed

[Anonymous No.15045125]

>>15045121
If they're intuitive then they must describe something. What is this something?

[Anonymous No.15045133]

>>15045125
groups of elements, which is something everyone has an intuition about

[NoFap Master No.15045151]

>>15043553
Literal retard speak.

[Anonymous No.15045153]

>>15045133
you are deluding yourself if you think that ZFC describe groups of elements "intuitively". I'd also like to hear what's intuitive about the axiom of infinity.
furthemore, there are groups of elements which don't exist according to ZFC, such as the group of all topological spaces etc.

[Anonymous No.15045156]

>>15043504
>IF YOU THOUGHT MY POLITICAL OPINIONS WERE CONTROVERSIAL, WAIT UNTIL YOU HEAR MY NEXT CONTRARIANISM
This is literally teenager tier

[Anonymous No.15045177]

>>15045153
>I say it's "mostly" intuitive
>BRO HERE'S ONE AXIOM THAT ISN'T
damn, looks like English comprehension also isn't intuitive for you

[Anonymous No.15045191]

>>15045177
You agree that the axiom of infinity is unintuitive then?

[Anonymous No.15045194]

>>15045191
No, infinity or boudlessness is something very intuitive to humans and that's why it has existed since forever in all forms of literature and religious practice

[Anonymous No.15045195]

>>15045121
unmeasurable sets are indeed very useful and intuitive, definitely not just masurbatory mathematical delusions

[Anonymous No.15045209]

>>15045194
have you ever seen an "infinite set" though?

[Anonymous No.15045219]

>>15045209
bait question, we are talking about intuitiveness and then you move the goalpost to "have you ever seen...?"

have you ever seen a rod of exactly length 5/4? no? then rational numbers don't exist.

[Anonymous No.15045236]

>>15045219
well, if you haven't, how can an axiom stipulating the existence of an infinite set be intuitive? I'm genuinely asking.

[Anonymous No.15045239]

>>15045008
The solution to the equation [math] x^2 = 2[/math]

[Anonymous No.15045244]

>>15045236
holy shit do you even know what "intuition" means?
intuition doesn't mean "shit I've seen" otherwise it would be called "experience".
nobody has ever seen infinity, but we intuitively have a concept of boundless things

[Anonymous No.15045249]

>>15045239
The equation has no solution.

[Anonymous No.15045253]

>>15045249
The field of complex numbers is algebraically closed due to the fundamental theorem of algebra, so every polynomial has a solution.

[Anonymous No.15045255]

>>15045209
A line is an infinite set of points.

[Anonymous No.15045277]

>>15045255
Leibniz: A point may not be considered a part of a line.
(Quoted in Rescher, 1967, p. 109)

[Anonymous No.15045283]

>>15045253
Bunch of verbal bullshit make no right.

Also, conplex numbers are pure non natural invention of human mind

[Anonymous No.15045284]

>>15045283
>Vectors are unintuitive

uhoh

[Anonymous No.15045285]

>>15045096
But I said "let". There fore it must Be

[Anonymous No.15045286]

>>15045253
There is no field of complex numbers. Its a fantasy. I challenge you to construct the field. You wont.

[Anonymous No.15045341]

>>15044214
>But the collection of ALL integers is problematic
What would be the the largest possible collection of integers in this case?

[Aether king of sci No.15045343]

0.999recurring is an infinite sequence derpaherf. You might be a haxxer but you're not a better mathy than me im gud.

Also recurring numbers are the only possible infinite sequences.

[Anonymous No.15045344]

>>15045286
>Vectors are fantasy

uh oh mathlet alert

[Anonymous No.15045345]

>>15045030
>Like your brain gives infinite a finite reservation of brain cells
I am not that anon, but I am interested in this claim. Could you be more specific on what you mean? Are you claiming you have evidence of a particular thought being ascribed a particular amount of brain cells? Do you believe you have evidence of a neural correlate to the thought of infinity?

[Anonymous No.15045350]

>>15045286
negative numbers are a fantasy

[Anonymous No.15045378]

>>15045156
You can tell his tiny pinch of fame has gotten to his head. He seems to think he's some sort of donald trump level personality where everyone gives a fuck about his opinions on everything and are waiting to be shocked at what he's going to say next. Just look at his profile photo, what an autist.

[Anonymous No.15045450]

>>15045283
>>15045286
>BTFOs finitards so hard they can't respond after 2 centuries

[Anonymous No.15045465]

>>15043504
>math
>i BELIEVE _____
Yep it's a CSchizo alright

[Anonymous No.15045482]

Lol.
The number 0,1234567891011... has all the naturals in it, it's somewhere between 0,12 and 0,13 on the number line.

[Anonymous No.15045502]

>>15045482
>has all the naturals in it
how do you know?

[Anonymous No.15045527]

>>15045502
That's the definition of the series. In sigma notation it's [math] \sum_{n=0}^{\inf} \frac{n}{10^n} [/math]
It's as real as pi or the golden ratio.

[Anonymous No.15045540]

>>15045502
He defined it this way worthless talentless trash, and it's a real number by definition

[Anonymous No.15045570]

>>15045540
>He defined it this way
so instead of constructing stuff from the axioms you basically create new unprovable axioms every time you want?

[Anonymous No.15045595]

>>15045570
Were you homeschooled?

[Anonymous No.15045603]

>>15045595
the point of the axioms is to have the smallest kernel of "arbitrary" statements about maths. if instead of constructing stuff with th eaxioms you simply "define" things into existence you are surrepticiously inventing more and more axioms out if thin air

[Anonymous No.15045831]

>>15045603
Are you a NEET? Why bother posting about something you have no idea about?

[Anonymous No.15045859]

>>15045831
Worse, this kind of people are sometimes and employed and have a whole interview dedicated to them
https://www.youtube.com/watch?v=_L3gNaAVjQ4

[Anonymous No.15045886]

>>15045125
> What is this something?
It is called the Von Neumann universe.
https://en.wikipedia.org/wiki/Von_Neumann_universe

[Anonymous No.15045897]

>>15045859
>>15045831
why can't losers who haven't read a single book about set theory and FOL just shut the fuck up? once the axioms are set if you can't constructively deduce a theorem then it's not a real result, it's just another axiom

[Anonymous No.15045964]

>>15045570
No, the series is defined as
[math] S_n = \sum_{k=0}^{n} \frac{k}{10^k} [/math]
And it can be defined as the sum of every number in the sequence
[math] a_n = \frac{n}{10^n} [/math]

The sequence b_n = a_n * 10^n is the sequence of natural numbers. Normally one would start from the naturals and apply the operations.

I know the whole "matching digits" operation isn't mathematical, so the sum I wrote which is concatenation of all the naturals would be something more like
[math] S_n = \sum_{k=0}^{n} \frac{k}{10^{(k*floor(log_10(k)))}} [/math]
the basic idea being the information contained within a single real number already is as much as the information contained in the entirety of natural numbers.

[Anonymous No.15046012]

>>15045603
The sequence
[math] a_n = n[/math]
is the sequence of natural numbers. This is the definition.
The sequence
[math] b_n = \frac{a_n}{10^n} [/math]
assigns to every element in the natural numbers an element in the rational numbers, because every element in the sequence is strictly inferior to the previous one is trivial.
The series
[math] S_n = \sum_{k=0}^{n} b_k [/math]
tends towards a real number if n tends towards infinity, a real number built out of a sequence containing all natural numbers.

The number 0.123456789101112... would be [math] b_n = \frac{a_n}{10^{n*log(n)}} [/math] and the log only taking discrete values, but the property is the same.

[Anonymous No.15046147]

>>15045345
Its a biological fact you have a finite amount of brain cells. Every thought is inheritly finite

[Anonymous No.15046178]

>>15043504
What a chad, I'm a finitist too

[Anonymous No.15046190]

>>15043598
>speaks of cardinality as if it's a concept applicable to the integers
Cardinality just means the size of a set

[Anonymous No.15046200]

>>15044116
>If there are no infinite sequence, surely every sequence has a last, final element
Yes
https://www.youtube.com/watch?v=edh5bbgSKqo

>Can any finitist on here tell me this number that they assert exists?
It is a number that it is physically impossible to write all the digits of

[Anonymous No.15046201]

>>15044139
>one logical argument for the nonexistence for the real numbers
Infinity doesn't exist in our world

[Anonymous No.15046204]

>>15044148
>Why can't I use base 2 or assign a symbol to this number and continue adding 1 to it?
Ask your computer

[Anonymous No.15046215]

>>15046200
Not watching a 1 hour retard shouting match.
>It is a number that it is physically impossible to write all the digits of
Define digit.

[Anonymous No.15046225]

>>15046147
I am not denying that. You didn't answer the question. I would like evidence that links specific brain cells to the creation of a specific thought or concept in a way that can be repeatedly demonstrated and for added bonus point, show how a completely different set of brain cells in two different people's heads can produce the same concept in two different minds to where we can know what one another are talking about, namely infinity in this case. Or, cut to the chase and tell me how a piece of objectively observable meat beams a non-objectively observable subjective experience into an observer. And explain why consciousness, if it is a physical object, can not be objectively observed as all other physical objects can be? What is the mechanism whereby this piece of meat actually transmits this non-material concept of infinity or any other concept to the experiencer?
point being pic related. Consciousness is not physical. Consciousness is made of consciousness, not brain or matter. Consciousness IS, because of a high level of immersion in the physical (virtual) world, constrained in certain ways by physicality that that can be observed and experienced neural correlatively, but that shouldn't be mistaken for consciousness being made of matter or it being a physical substance. So the number of cells in a physical (virtual) brain is irrelevant to what a mind can conceive of. In point of fact, brains, as is all other matter, are only ever observed as MENTAL OBJECTS in minds. And this by the way is why infinities are grounded in minds, not in the physical world. No infinities in the physical world, no continuities, no analyticity. These things reside only in models that can be mapped on to the physical world in some cases to make predictions to non-arbitrary precision.

[Anonymous No.15046248]

>>15046215
>Define digit
Hindu-arabic numeral

[Anonymous No.15046249]

>>15046248
Why can't I write numbers using Roman numerals?

[Anonymous No.15046315]

>>15046190
Exactly my point.
Finitists wouldn't talk about the cardinality of the integers since they disagree with "the integers" being a set in the first place.

[Anonymous No.15046365]

>>15045341
There isn't one. Just like there isn't a largest number.
Why does there need to be a largest one?

Under finitism, sets can be arbitrarily large, just not infinitely large.

If you believe that sets shouldn't even be allowed to be arbitrarily large, then you're stepping into strict finitism/ultrafinitism.
In that case, "the largest possible collection" may or may not be sensical and what that collection is will depend on you motivations for subscribing to ultrafinitism.

[Anonymous No.15046386]

>>15046365
>Why does there need to be a largest one?
If a sequence is finite, then for some n there are no more numbers after that. Otherwise, it would never end and therefore be infinite. This is exactly equivalent to the statement that there exists a number [math]n[/math] such that [math]n[/math] is the last number in the sequence.
If there is no last number, then the sequence must be infinite, since if you were to count each member of the sequence, you would never reach the last one.
>sets can be arbitrarily large, just not infinitely large
This is a meaningless statement. If it's not infinite, then it must be finite (by definition) and therefore the number of elements in the set has to be a precise number.

[Anonymous No.15046462]

>>15046386
>If a sequence is finite...
I'm not the person who talked about sequences. But I'll try to answer your question.

>If there is no last number, then the sequence must be infinite
Correct. But what's you're point?
Even though there is no last number under classical finitism, there is also no such thing as the sequence of all numbers.
Since all sequences have to be finite under finitism, you can only have incomplete sequences of numbers.
So no contradiction.

>This is a meaningless statement
I don't know what to tell you if you don't distinguish between arbitrary large and infinitely large.
Are you familiar with Aristotle's concepts of potential vs. actual infinity?

> If it's not infinite, then it must be finite (by definition) and therefore the number of elements in the set has to be a precise number.
Yes, that's what arbitrary large means. Every set has to be finite, but it can be any finite size you like.
Under classical finitism, you could have a set with 1 element, a set with 10 elements, a set with 10^10 elements, or even a set with 10^(10^(10^(10^(10^(10^10))))) elements if you want. As long as the size is finite, you're good.

[Anonymous No.15046483]

>>15046225
Consciousness is related to the brain. Like computer literally and physically reserves bits 0 1111 00000... for positive infinity, similarly your brain reserves something to represent infinity. Should it be symbol 8 rotated 90 degrees, trying to think furthest edge of universe... you just reserve some thought, reserve say a ten thousand brain cells. But its not real. Same with magic elves, you can think about something, like an elf cap. Remember about some TV show about them, lurking in your brain cells in your memory system.
But it doesnt make them real.

[Anonymous No.15046497]

>>15046462
>Correct. But what's you're point?
If you agree with this, and claim that the sequence [math]a_n = n + 1[/math] is finite, then you have to be able to point out the last number of the sequence.
>there is also no such thing as the sequence of all numbers
I just constructed a sequence containing all the positive whole numbers above, so this claim is at the very least false for the set of positive whole numbers. It's also trivial to construct a sequence containing all whole numbers.
"Arbitrary largeness" is irrelevant.

[Anonymous No.15046504]

>>15046249
You can

>>15046315
Integers are all the numbers between the least possible integer and the biggest possible integer that can be written within the universe constraints (like the number of atoms per second a computer could compute)

[Anonymous No.15046513]

>>15043504
Tell him to stop stealing my ideas.

[Anonymous No.15046521]

>>15046497
>then you have to be able to point out the last number of the sequence.
Why?
Couldn't a proof exist without needing to provide this value?
Suppose the final value is too large to be written in this universe, but still finite.
So you wouldn't accept reality because that number couldn't be written out for you?

[Anonymous No.15046546]

>>15046504
Take the Roman numerals and write the largest possible number in them. Now, let us construct a New Roman numeral system such that [math]\alpha[/math] indicates this largest possible number. This is possible because you claim that this number not only exists, but can be written down; it's a number just like 5, which is indicated by V in the Roman numerals. Now let us write down the number [math]\alpha \text{I}[/math]. I just wrote down a number that is exactly 1 larger than the largest possible number, which leads us to a contradiction.

[Anonymous No.15046560]

>>15046546
Actually since a sequence ending ...IIII isn't a valid Roman numeral, and nor is ...IVI, ...IVIIII, and ...IXI isn't, you have just submitted an invalid procedure.

[Anonymous No.15046565]

>>15046560
I didn't write any of those, retard.

[Anonymous No.15046599]

>>15046497
Finitists wouldn't accept "a_n = n+1" as a sequence.
They would probably consider it a rule that can be used generate arbitrarily large sequences.
Assuming a_1 = 1, applying the rule once will give you the sequence "1, 2".
Applying the rule 8 times will give you the sequence "1, 2, 3, 4, 5, 6, 7, 8, 9".
Applying the rule any finite number of times will give you a finite sequence.
Finitists would argue that you can't apply the rule infinitely many times and therefore won't be able to use that rule to generate an infinite sequence.

You're arguing as if all the constructions/definitions that are normally accepted are also accepted under finitism, but that's exactly what finitism (and other philosophies of math) are questioning. Philosophy of math is about questioning what the rules of math should be and what they mean.

[Anonymous No.15046622]

>>15046504
>biggest possible integer
You seem to assume strict finitism as opposed to classical finitism.
Under strict finitism, there is at least 1 more rational* number than integers (i.e. 1/2) , so they would have different cardinalities and OP's claim would be wrong.

*: I'm using rational number instead of real number since I have no idea what a real number is under either finitisms.)

[Anonymous No.15046649]

>>15046599
>>15046622
There is no such thing as "under finitism", you braindead retard. Either it's true or it's not.

[Anonymous No.15046685]

>>15046649
Sure, but I don't know which philosophy of math is "true".
So until then, I'll work with hypotheticals and use the expression "under..." to specify which hypothetical I'm currently using.

[Anonymous No.15046711]

>>15046365
First check your definition of an "arbitrarily large" brainlet, let me remind you.

"For arbitrarily large x, p(x) holds" or
[eqn]\forall{n\in\mathbb{R}}\;\exists{x\in(n, \infty)}\;\;p(x)[/eqn]

But if you check for the natural numbers you still have a contradiction. (hint: inductive reasoning)

[Anonymous No.15046754]

>>15046711
That definition doesn't quite work under finitism since it assumes that the real numbers is a set.
But you can modify it slightly in a way that I think preserves the intention: for any natural number n, there exists a set x such that, ||x|| > n".
That claim would be true whether you allow infinite sets or not.

You do know that the order of the quantifiers matter right?
For example, the claim "there exists a set x such that, for any natural number n, ||x|| > n" is true if you allow infinite sets, but false if you don't.

Maybe this will help you: https://en.wikipedia.org/wiki/Arbitrarily_large#Arbitrarily_large_vs._sufficiently_large_vs._infinitely_large
In particular: Furthermore, "arbitrarily large" also does not mean "infinitely large". For example, although prime numbers can be arbitrarily large, an infinitely large prime number does not exist—since all prime numbers (as well as all other integers) are finite.

[Anonymous No.15046767]

>>15046754
Let there be a set of the real numbers, here you go I provided a definition

[Anonymous No.15047249]

>>15045030
>well defined
Congratz you checkmated yourself, AGAIN. I recognize your stupidity. Im not 100% sure which retard you are....but I know you, mf...

[Anonymous No.15047255]

>>15045030
>>15047249

Oh, and to give you a hint. Computers and "well defined" do not mix, almost 100% ever, with a few exception for even powers and such.

t.Studied Computer Archetecture

You box cant "do" maths, just the one, and its rounds off or has to do waaay more calculations for the rest. Heh...."well defined", you should learn how computers "do" math.

No more hints for you...now I post space laser memes because I btfo of you.

[Anonymous No.15047259]

>>15046565
>I didn't write any of those, retard.
You submitted an invalid procedure as part of a proof. I offer "IV" as a candidate largest number. You reply with "IVI" to supposedly prove me wrong, but that isn't a number in the system of Roman numerals.
It's as if you say N+chicken is a bigger number than any N that I offer, and so I quite understandably call you an idiot.

[Anonymous No.15047269]

>>15045121
It took 22 years of intense group masturbation by professional autists to get from Zermelo set theory to Zermelo–Fraenkel set theory.
First-order logic, the background for ZFC, was also being developed/standardized as a formal logic during that time (and even after).

I think that ZFC is a solid foundation, but claiming that ZFC is mostly intuitive is disingenuous imo.
There are a lot of little quirks that might seem weird for someone who hasn't seen a formal theory before (on top of formal theories being an unintuitive concept to begin with):
What are the elements? What do you mean there's only sets?
If everything is a set, what's a natural number? What's an ordered pair? What's a function? What's a sequence?
Why do we need the axiom of extentionality? Why don't we need its converse? What's being extended?
Which axiom do you use to make singleton sets. How can you make a set with 3 elements?
How do you get the union operation from the axiom of union?
How do you know what set you get from the axiom of infinity?
How do you get the set of all natural numbers from the axiom of infinity?
Why is specification/replacement an axiom schema instead of just an axiom?
What's a "well-defined" predicate/function? Is a formal function different than a "normal" function (which is actually a set)?
Why can specification/replacement be applied on infinite sets?
Why can specification/replacement be applied using undecidable/uncomputable predicates/functions?
Why can power set be applied on infinite sets? Why are we ok with a set containing elements that are undefinable? What's a real number?
How do you relate the formal statement of the axiom of regularity to this informal formulation: "A set contains no infinitely descending chains". Wouldn't A := {B} and B := {A} satisfy the formal statement but be an infinitely descending chain anyway?
Axiom of choice...

[Anonymous No.15047277]

>>15047259
>You reply with "IVI" to supposedly prove me wrong
No, I write a single number, [math]\alpha \text{I}[/math], illiterate retard.

[Anonymous No.15047278]

>>15047269
>Axiom of choice...
I stopped here, not gunna read any more.

[Anonymous No.15047405]

>>15043504
Then what is this supposed cardinality?
What is the largest number, George?
You going to do some other sort of sleight of hand and just trying to replace infinity with aleph_0 like its not the same thing?

[Anonymous No.15047425]

>>15043553
>I don't think a dynamic set of electrons is a set

[Anonymous No.15047485]

>>15047269
>There are a lot of little quirks that might seem weird
that's why I said it's MOSTLY intuitive holy shit.
the reason why those quirks exist is because the purely intuitive definitions led to paradoxes, so we had to adjust them a little bit.
if you simply read a decent book about set theory that explains this process everything would seems logical

[Anonymous No.15047538]

>>15043600
So which numbers are the good ones are which are the bad ones?
What is 95% of the cardinality of the integers?

[Anonymous No.15047545]

>>15043690
(2/1)^(1/2)

[Anonymous No.15047547]

>>15043786
pi, i, e

[Anonymous No.15047553]

>>15047547
but we can compute them up to an arbitrary length, which is the only thing that matters since we don't have infinite precision with our scientific instruments

[Anonymous No.15047562]

>>15047553
Those values aren't arbitrary in length though, if you are calculating something arbitrary, you aren't actually calculating those numbers, you are just making estimates based on the limits of your computer.

[Anonymous No.15047570]

>>15047553
Also you can't even compute i to any arbitrary length, it is what it is in an ALU by definition, not by computation.

[Anonymous No.15047577]

>>15047570
"i" is just a symbol to identify a certain direction. it's only used because you can change its sign by squaring it so it simplifies calculations, nobody cares about it's actual "value"

[Anonymous No.15047589]

>>15047577
>a certain direction.
No, it represents the incompatible value of sqrt(-1), obviously since you can't calculate it and it directly disproves you claim that every number is calculable, you are going to pretend it doesn't actually mean anything that anyone cares about.

[Anonymous No.15047593]

>>15047589
>incompatible
*incomputable

[Anonymous No.15047603]

>>15043598
>>15047405
It's not too off.
He can e.g. proclaim that only finite sets exist and that there's a class function putting (something which is classically as big as) N and R into bijection.

[Anonymous No.15047604]

>>15047589
"i" is never used as a number, it's only useful when interpreting it as a rotation of some sort. nobody builds a bridge and has to calculate "i" up to a certain decimal digit. all of its uses relate with the angle it forms on the complex plane (which is computable), not with its value

[Anonymous No.15047616]

>>15047604
That seems like a fun way to cope with the fact that you will never calculate i.

[Anonymous No.15047622]

>>15047603
Ok, so what is this big number you are alluding too, why keep us in suspense?

[Anonymous No.15047624]

>>15047604
You do realize that is all the case because i can't be calculated and bridge builders are just doing the best with the limited resources they have, right?

[Anonymous No.15047629]

>>15043680
they have the right to be.
Mathfags invented the worst syntax for logical expressions possible

[Anonymous No.15047632]

>>15047616
>you will never calculate i
provide ONE real life example where i needs to be calculated instead of using it as a handy symbol for rotation

[Anonymous No.15047633]

>>15045022
no such thing as infinity

[Anonymous No.15047636]

>>15047632
Why would their be real life examples for using something that is unknown and incalculable?

[Anonymous No.15047641]

>>15047636
so you are telling me there is no real life examples of a calculation being hindered by the fact that the value of i is unknown?

[Anonymous No.15047646]

>>15047632
>>15047636
>>15047641
Provide me a single real life example where the value of 1 is calculated. What is 1 equal to?

[Anonymous No.15047658]

>>15047622
Why do people have such a hard time with unknowns. You don’t have to know how large the universe is to say that you believe it is not infinity

[Anonymous No.15047668]

>>15047658
The problems is that OP is specifically saying it isn't unknown, he knows it is some finite number, its not that people are having a hard time with it, its that some charlatan is coming along making up lies he is unable to back up.

[Anonymous No.15047672]

>>15047646

[Anonymous No.15047682]

>>15047672
That doesn't calculate the value of 1.

[Anonymous No.15047707]

>>15047682
It calculates the value of 1 to prove 1+1=2.

[Anonymous No.15047725]

>>15047646
"1" is a character that symbolizes that two objects have the same magnitude (once a measure is defined).
if we want to measure length, we take a reference object and assign it the length of "1" and then compare it with every other object we want to measure. if they measure "1" it means they have the same length as the reference.

in the real world we have defined "1" in terms of invariant natural phenomena such as the speed of light or atomic weight or other stuff. 1 meter is the time it takes for light in a vacuum to travel a certain distance, and so on.
once you've defined "1" for every basic unit of measurement you automatically have defined "1" for all of them since the remaining ones are combination of the basic ones.

any other interpretation is deeply schizophrenic

[Anonymous No.15047806]

>>15047707
>It calculates the value of 1
It doesn't.

[Anonymous No.15047807]

>>15047725
So what's the calculated value of 1?

[Anonymous No.15047809]

>>15047725
>if we want to measure length, we take a reference object and assign it the length of "1" and then compare it with every other object we want to measure. if they measure "1" it means they have the same length as the reference.
This is literally true for any number mouthbreathing retard.

[Anonymous No.15047811]

>>15047485
And yet you can't explain what a set is even though it's so intuitive.

[Anonymous No.15047812]

>>15047807
The calculated magnitude of the reference object with length 1.

[Anonymous No.15047822]

>>15047812
>The calculated magnitude of the reference object with length 1.
Which is? LOL. You people are so braindamaged it's unreal.

[Anonymous No.15047834]

>>15047822
The magnitude in question.

[Anonymous No.15047838]

>>15047811
it's a collection of objects, which is something every humans has an intuitive understanding of
>inb4 what is a collection of objects
every single axiomatic system, be it set theory or whatever garbage Wildburger comes up with, will not be able to properly define its primitive definitions. an object is an object, a collection is a collection, a string is a string, a segment is a segment.

if you think this "gotcha" shit works then provide one axiomatic system where you can definitely answer every single "but what *is* xyz" forever without resorting to intuition

[Anonymous No.15047840]

>>15047838
>it's a collection of objects
There are many collections of objects which are not sets. There are also sets which are not collections of objects. You are wrong.

[Anonymous No.15047841]

>>15047809
except numbers don't exist in real life

[Anonymous No.15047843]

>>15047485
>this is mostly intuitive
>just read the user manual AND patch notes
do you know what intuitive means?
having to read/ask about it or conciously reason about it is exactly what makes it unintuitive, regardless of how logical it is.

[Anonymous No.15047844]

>>15047822
>Which is?
You were literally JUST TOLD what it was.

ENGLISH, LEARN IT.

[Anonymous No.15047847]

>>15047834
>>15047844
>being this mentally ill

[Anonymous No.15047850]

>>15047840
>There are many collections of objects which are not sets.
this is because certain collections of objects generated paradoxes, this is why the axioms were made to specifically put some limits on the intuition and exclude these kinds of collections.
you have never opened a set theory book, you're a fucking retard unable to argue a single point

[Anonymous No.15047853]

>>15047843
provide ONE SINGLE axiomatic system that doesn't rely on intuition, I'll wait

[Anonymous No.15047858]

>>15047850
You've said that set = collection of objects. That's wrong. So, what is a set?
Which set theory book explains what is a set?

[Anonymous No.15047860]

>>15047847
>Gets called out, responds with "You're fucking crazy, man!"

ANON, WAKE THE FUCK UP.

[Anonymous No.15047863]

>>15047858
a set is a collection of objects, ZFC axioms specify better what kind of sets don't create paradoxes that fuck up modern maths. it's really that simple, must be horrible to be as stupid as you

[Anonymous No.15047867]

>>15047860
Still waiting for you to calculate 1. All this legit psychiatric rambling about "calculating" the magnitude of an object with length 1... this is legit grounds for a ban.

[Anonymous No.15047869]

>>15047853
Most of them? including ZFC?
I rather have my axiomatic systems rely on logic than intuition.
I want to use axiomatic systems to do math, not philosophy.

[Anonymous No.15047874]

>>15047869
explain what a set is without using human intuition

[Anonymous No.15047877]

>>15047867
>Still waiting for you to calculate 1
One is based on what ever the fuck you say it is, YOU ARE NOT A MATHEMATICIAN.

"Calculate", mother fucking its a symbol for a complete unit, what base system youre using is how many piece it makes up of. I use base Infinity, so its completely dynamic and easily calculated using baseless metrics.

You....wouldnt know anything about that, you have a second year students unseestanding of Maths, at best.

>psycho
>schizo
>ramblings

WAKE THE FUCK UP, MIDWIT. YOURE NOT WELCOMED HERE.

[Anonymous No.15047881]

>>15047863
The collection of all groups doesn't fuck up modern maths at all, it's a very common object. It is undeniably a collection of objects. Why is not a set then? You have no other explanation than "because an ad hoc axiom says so". That's not intuitive nor rigorous.

[Anonymous No.15047890]

>>15047877
So you can't calculate 1? 1 is just 1 and that's all it is?

[Anonymous No.15047897]

>>15047874
Do you want me to explain what the philisophical concept of a set is?
I can't do that without human intuition.
In fact, I don't think I would need to do anything at all since I agree that this concept is intuitive.

Do you want me to explain to a person who knows what first-order logic is what the default defintion of a set is in math?
For that I would just copy paste the zfc axioms. No human intuition needed. Even a computer can manipulate formal statements.

Do you want me to explain why I think the zfc axioms do a good job at approximating the philisophical concept of sets?
Then I'll need human intuition, but also logic.

[Anonymous No.15047899]

>>15047890
>So you can't calculate 1?
You're askng for something that doesnt exist then struting around like youre a champion when no one can present it.

>Show me a circular straigh line.
>lol no thats a circle, not a straight line, lol no thats a line, not a circle
You lost, you charlatan jackass.

YOU WILL NEVER BE A MATHEMATICIAN.

[Anonymous No.15047901]

>>15047899
We agree that it makes no sense to talk about "calculating 1". Why are you mouth breathings talking about "calculating i"?

[Anonymous No.15047916]

>>15047897
>Do you want me to explain to a person who knows what first-order logic is
you're just shifting the burden. FOL cannot be explained without intuition, therefore set theory can't.

[Anonymous No.15047922]

>>15047901
I only see you doing this retardation, and being unable to squash it, as there is no calculate except by the base applied to it. Youre asking for so.ething thats pre-calculated and is used to formulate calculations.

Again, you couldnt see the errors in all of this, so stop acting smart.

>Gets owned.
>lol hehe no I was on your sode the whole time, "merely pretending to be a retarded"

TOURIST. LEAVE.

[Anonymous No.15047953]

>>15047916
FOL is a formal logic, it only requires formal/mechanical manipulations. A computer can do it. The only intuition you need is strings, which I take for granted. If you can't even process letters then any communication via text is impossible, I wouldn't even be able to talk to you, let alone explain something.

[Anonymous No.15047956]

>>15047953
>The only intuition you need is strings
exactly, FOL can't exist without an intuitive understanding of what a string is and as such set theory can't exist too

[Anonymous No.15047972]

>>15047956
are you >>15047485

If so, you started with "mostly intuitive" and my last post conceeded to "requires the bare minimum amount of intuition needed for communication via text between humans".
You do understand how those are different right?

[Anonymous No.15047986]

>>15047622
>Ok, so what is this big number you are alluding too
First time I had posted in the thread

>>15047881
In raw predicate logic, if E is any relation, you can quickly prove
[math] \forall x. \big(xEs\leftrightarrow(xEy \land \neg xEx)\big) \to \neg(yEs\lor sEs\lor sEy) [/math]

For any set, if you allow for (even just predicative) comprehension, so that "x not in x" is a valid predicate, then you can define
s := {x in y | x not in x}
and the above logical statement implies
s not in y.

So very moderate forms of comprehension principles have the consequence that the collection of all sets is not consistently a set (because given a candidate y, you can define some s that is definately not in it).

It's fairly easy to defined more collections which can't be sets (e.g. the collection of all ordinals.)

Now with algebraic structure, the issue is that in set theory they are generally defined as "set + function", e.g. a group is any set plus any operation fulfilling some axioms.
But now given any set t, the pair ({t}, id) with id(t)=t is the trivial group.
So given any class y, you can define the class y' which for every x in y holds the group ({x}, id). So there's many collections of trivial groups.
So because there's collections which aren't sets (by predicative comprehension), the "set plus structure" concept is quickly infected by this issue.

Btw. very quickly people had also developed foundations where "x is not in x" is not a legal predicate for comprehension

https://en.wikipedia.org/wiki/Stratification_(mathematics)

but I mean the ZFC deal was fairly quickly settled on and few mathematicians care about foundations

[Anonymous No.15048001]

>>15047972
Set theory is based on the intuition about what a "set" and what "∈" are. If you don't get them then set theory won't make any sense.
ZFC set theory is additionally based on another type of intuition, "given the definition of a set, what does it mean to take the union of two of them?".
there are many ways to define what the union of two sets is, and ZFC uses a pretty intuitive one that most people will find reasonable.
Then there are axioms such as the axiom of Choice that are not intuitive at all but are needed to prove some important results so it had to be added even though nobody would have conjured it up from scratch

[Anonymous No.15048009]

>>15043587
>algebra anal top
lewd

[Anonymous No.15048010]

>>15047890
We define 1 as the identity element of multiplication, i.e. it is a number such that [math]1 \cdot \alpha = \alpha[/math].

[Anonymous No.15048034]

>>15048010
>define
Not a calculation. Legit psychiatric rambling, mods should ban you.

[Anonymous No.15048036]

>>15048034
>I never studies first order logic OR have taken a few courses in math

Uhoh schizo stop projecting

[Anonymous No.15048047]

>>15047922
>I only see you doing this retardation
See >>15047646 and kill yourself.

[Anonymous No.15048052]

>>15048001
We were using different definitions of intuitive.
From the cambridge dictionary, you seem to be using definition 1 (which I agree mostly applies to all mathematical definitions, even the axiom of choice) while I was using definition 3 (which I still think zfc does not mostly satisfy).

[Anonymous No.15048069]

>>15043787
the first reply was right
not understanding something makes you dumber, not smarter
if you realize that you don't understand and make an attempt to then you have something to be smug about
don't be smug in your ignorance

[Anonymous No.15048095]

I just calculated 1.
Its approximately equal to 1.000000...

[Anonymous No.15048098]

>>15048047
>See >>15047646 and kill yourself.

Looks EXACTLY the same as >>15047901


NO U KYS

[Anonymous No.15048103]

>>15048095
Finally, we're getting somewhere. Thank you, Anon, for an actual substantive post.

[Anonymous No.15048156]

>>15043504
The universe is not discrete, it's continuous. If the universe had a smallest unit and a discrete topology then the spin of particles would imply there exists non trivial integer solutions to equations of the form a^4 + b^4 = c^4

The universe has no smallest length or unit (the Planck length is not the smallest unit) spacetime is continuous.

[Anonymous No.15048160]

>>15048156
Note also that this means the universe can not be modeled on a Turing machine

[Anonymous No.15048197]

>>15048034
What is a calculation?
You cannot express 1 as an algebraic equation because algebraic equations already presuppose the existence of number 1. It has to be constructed along the group and/or stated as an axiom.

[Anonymous No.15048202]

>>15043504
I don't know what any of that means.
>t. CS major

[Anonymous No.15048213]

>>15048098
The danger of having "people" like you around is that you provide justifications for state-enforced eugenics.

[Anonymous No.15048258]

>>15048213
Answer; >>15048197

DO IT OR KYS.

[Aether king of sci No.15048282]

REPEATING NUMBERS EXIST
THEY ARE AN INFINITE SEQUENCE

[Anonymous No.15048302]

>>15043504
>Finitist
>"The integers"

[Aether king of sci No.15048306]

>>15048282
There is only one infinite sequence: repeating number.

[Anonymous No.15048431]

>>15044148
Why can't I just do:
[math]
\frac{1}{0} = \alpha
[/math]
Checkmate mathcucks, dividing by zero is indeed possible.

[Anonymous No.15048446]

>>15048431
>dividing by zero is indeed possible
See pic; >>15048103

Why yes, of course it is.

[Anonymous No.15048586]

I always knew CS people were mid-IQ but I honestly didn’t realize just how mid-IQ they really are. That’s on me.

[Anonymous No.15050028]

>>15048302
that's what meth does to your brain

[Anonymous No.15050059]

>>15044116
It's equal to n+1 where n = max(Z)

[Anonymous No.15050111]

>>15044207
Calculated means determined by a mathematical calculation or reasoning.

Arithmetic is the branch of mathematics that deals with the manipulation of numbers, typically using addition, subtraction, multiplication, and division.

An integer is a whole number, meaning it is not a fraction or a decimal. It can be positive, negative, or zero.

A number is a mathematical concept used to represent a quantity in a mathematical system. There are many different types of numbers, such as whole numbers, integers, rational numbers, and irrational numbers.

[Anonymous No.15050113]

>>15048197
A calculation is the process of using mathematical operations, such as addition, subtraction, multiplication, and division, to determine the value of an expression or solve a problem. Calculations can be done by hand or with the aid of a calculator or computer.

In algebra, equations are used to describe relationships between different quantities, and the goal is to find the value of an unknown quantity that satisfies the equation. In this context, the number 1 is a constant that is already defined and does not need to be constructed. It is often represented by the symbol "1" in equations and expressions, and it has the property that it is the multiplicative identity, meaning that any number multiplied by 1 is equal to that number.

[Anonymous No.15050120]

why do we have to say infinities "exist" (wtf does exist mean anyway?)

can't we just say if you have a finite series, you could add one more term, proceeding by some rule? iirc the whole magic of real analysis class was epsilon-delta proofs of that nature

[Anonymous No.15050156]

>>15043504
Cantor's diagonal argument is really the epitome of pseud cattlemonging brainlessness.

[Anonymous No.15050161]

>>15050120
numbers exist

[Anonymous No.15050168]

>>15050120
Infinities are a computational ideal used to implicate series. It is important to note that there exists no pure concept for the principal of iteration.

[Anonymous No.15051586]

didnt this retard compare the ability to perform a buffer overflow attack to having a sniper rifle in your closet?

[Anonymous No.15051770]

>>15043614
>unironically go outside and touch grass
Go back

[Anonymous No.15051857]

>>15043504
>says something objectively true
lmao realtards will forever cope
real number are obsolete and are largely a parlor trick of math
Realtards have to options
1, accept finitism
2, accept the Enochian infinite finitist definition of reals
once again Enoch proves himself as supreme

[Anonymous No.15053412]

>>15046190
what's the size of the set of integers then anon?

[Anonymous No.15053460]

>>15053412
There's no "the set of integers", anon. There are infinitely many integers in the sense that if you have any (meaningful i.e. finite) set of integers, you can always find another integer which is not your set. That doesn't mean you can organize "all" integers into a set and treat it as a completed object.

[Anonymous No.15054745]

>>15043787
>what's the extra D for?

[Anonymous No.15054779]

>>15044116
2 ^ the number of Planck areas on the surface of a black hole containing all the matter-energy in the universe - 2

[Anonymous No.15054788]

>>15045008
Create an isosceles right-angled triangle whose shortest sides are both of length 1. Sqrt(2) is equal to the length of the hypotenuse of that triangle. If this doesn’t prove the existence of sqrt(2), then you can’t prove the existence of any number.
And anyway, if you believe in the integers, you already believe in an infinite sequence. Consider the trivial sequence constructed from the positive integers:
>S(n) = n for all n ∈ a+
George Hotz is a cumbrain.

[Anonymous No.15054977]

>>15047269
Right, it you typed that on a device based on quantum field theory.

[Anonymous No.15054980]

>>15043791
literally no one has ever said "lmaoing"

[Anonymous No.15054986]

>>15047616
[math]
\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix} ]/math]

[Anonymous No.15054988]

>>15047616
[math]
\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix} [/math]

[Anonymous No.15054994]

>>15045008
>>15047616
[math]
\begin{dvmatrix}
0 & 1 \\
1 & 0 \\
\end{dvmatrix} [/math]

[Anonymous No.15055003]

>>15045008
[math]
\begin{Vmatrix} 0 & 1 \\ 1 & 0 \\ \end{Vmatrix}
[/math]

[Anonymous No.15056566]

>>15043787
Blown The Fuck OuteD

[bodhi No.15056881]

>>15054980
they say lol'ing

pwnd chud

[Anonymous No.15057275]

>>15045378
He may certainly be autistic, but most of his opinions are definitely based.

[Anonymous No.15058566]

>>15047672
Principia Mathematica only goes to show that trying to create a consistent mathematical system purely based on human thinking is a lost cause. Computers pretty much accomplish what the writers wanted to accomplish with the book. Computers are superior as mathematical systems because they build on physical application of logic gates, instead of human thinking which is prone to errors and baseless assumptions.

[Anonymous No.15059835]

>>15043504
build reals in ZFC
ZFC is first-order
by Skolem, there's a countable model

simple as

[Anonymous No.15060297]

Claiming that sqrt 2 doesn't exist is retarded, but uncomputable numbers seem like bullshit.

[Anonymous No.15060306]

>>15060297
sqrt(2) will exist in my heart when an anon show me how to measure the in-commensurable portion and not just hide behind the radix

[Anonymous No.15060319]

>>15043680
> there's also this phenomenon of young (especially Silicon Valley) programmers going on far too dangerous hikes and dying.
After dealing with programming bullshit all week sometimes you just want to get lost in the wilderness. Silicon Valley as the name suggests is surrounded by mountains full of technical trails.

[Anonymous No.15060321]

>>15060297
>but uncomputable numbers seem like bullshit
Easily happens if your logic allows for Comprehension.

>Let e be an enumeration N->String of all computations in a language (say Turing machines, lambda expressions, legal C++ programs of the form main(){foo} where foo is a legal C++ expression)
>let u be the number which is decimal expansion starts with 0. and the n'th digit equals 0 if the computations e(n), when ran, eventually halts and 1 if it never halts
Assuming LEM, this is a functional assignment and each digit is either 0 or 1.
Then u is a real in the interval [0,1].
It's not the case that for all n, we can compute the n'th digit of d.

What's worse, you can't take the computable numbers as a collection and expect they have good properties, where "good" means e.g. the hopeful closure properties you find in the theory of the reals

https://en.wikipedia.org/wiki/Specker_sequence

[Anonymous No.15060326]

d=u, I changed notation midway

[Anonymous No.15060355]

>>15048431
you can divide by 0 in the trivial ring and your alpha and 1 are both 0

[bodhi No.15060367]

Im the best programmer alive

[Anonymous No.15060401]

mathematical concepts don't have to be "measurable", they have to be free of contradictions

[Anonymous No.15060787]

>>15048156
a discrete spacetime invariably breaks all the other continuous symmetries in physics, too. the lorentz symmetry for example has been experimentally verified at distances 100x shorter than the planck length
https://arxiv.org/abs/0908.1832
you'd need creationism levels of fine-tuning to get around it

[Anonymous No.15061283]

>>15043824
>Then it can be anything
Yes exactly. Are you stupid? You can literally look at people inventing mathematics in a variety of ways throughout history, according to their beliefs, needs, and traditions. You know you can alter it and change how it works. You know you can create more. You know it can be incompatible and operating on a different basis.