My math professor told us that real numbers don't exist. Is he trolling?
not if its wildberger
either way hes full of it
Does 3 "exist".
The answer depends on how you define "exist", and experience shows you can waste a lot of time discussing this.
>>7694614
Does "3" exist?
Lets go back in time to the time of the greeks, before we abstracted our number system to make it more useful and we still defined everything around geometry.
Define the unit segment. Just draw a straight segment on a piece of paper and call it the unit.
Can you draw a segment 3 times as long as the unit segment or draw 3 unit segments and put them together in one longer segment? The answer is yes.
So the number 3 exists.
That quantity that we define as three exists and can be observed in nature. Three pinecones, three coins, three dogs, etc.
Obviously, you don't have to call it "three," and the word "three" is only as real as any other word.
>>7694662
tautology
>>7694601
Math doesn't exist per see, It's just a really complex meme
>>7694670
What are you trying to say?
>>7694672
that you are an idiot
>let's define 1 to be 1
>>7694601
define 'exist'
>>7694674
That is not what I said.
Tell me, how do you think mathematics started huh?
Anyways, I am not defining 1 to be 1. That is exactly why I took my argument to geometry, completely ignoring our more abstract representation of the number line.
You can define the unit to be anything. I even told you how to. Get a pen and draw a straight line. It doesn't matter what length. Then, after you have created your line, call it your unit.
Then you can draw a line 3 times as big.
I am taking a real, geometrical object and defining that as 1. Not taking 1 and defining it as 1. 1 could be anything as long as you can construct things from it.
Are you retarded?
>>7694671
math is theoretical so it exists in the same way gravity or electromagnetism exists
scientifically theoretical things exist so he is definitely trolling
>>7694681
tautology
>how do i prove 3 is real? because you can triple 1 and get it
>how do i prove one is real? because i can triple it to get 3
just fuck off undergrad
>>7694689
He's right you know. I know you might not realize it, but it has less to do with what you're saying, and more to do with you constructing and explaination of a concept by using a related concept. It lacks an ultimate explaination. Basically, give up, there's no point.
>>7694689
Are you trolling right now? Do you really not get what I am trying to explain to you?
First, I am not talking about numbers. I am talking about segments. That is how we used to define numbers, until it became an outdated method when we discovered irrational numbers.
Also, I am not claiming that 3 "is real", I am claiming that you can construct 3.
And I am not claiming one is real because i can triple it to get 3. I am claiming that you can construct a unit by drawing something.
Lets be retarded for a second.
Lets forget segments to illustrate that the unit can be anything.
Instead of a segment draw a triangle of any size. Call this triangle your unit.
(Side node: The greeks did not consider 1 to be a number. They just used it to construct the other numbers)
Then draw or imagine a triangle 3 times as big as your unit triangle. That is your "3".
3 is not really real but you can construct something that makes sense to call it 3.
>just fuck off undergrad
Is there a problem? Is your ego too big to accept knowledge from someone younger than yourself? This is how ignorant people are produced. Thinking that you are too good to accept ideas from other people.
>>7694704
this entire post reeks of underage
>3 is not really real
refer to your first post, nice backpedaling
>>7694707
In my first post I said 3 exists.
In my last post I said that you can construct 3.
If you can construct it then it exists.
Tell me, big guy, do squares exist?
>>7694707
Come on man, you're gonna make him hurt himself. I just hope one day he understands that his 'unit' is the invented idea of a numerical ideological figure.
This is a discussion suited for philosophy rather than mathematics.
>>7694614
This guy is right.
Once we have proven or disproven the existence of real numbers in the physical sense, what have we learnt?
Nothing, absolutely nothing of use.
Even if they do not exist, we can still continue to play around with their properties in mathematics.
>>7694714
you missed the point entirely, re read my previous replies and re examine your tautology
>>7694715
I dont know who to stick up for anymore. One is just repeating underage and not explainin the error, and the other is asking if squares exist to prove that 3 exists.
>http://www.4chan.org/rules
2. You will immediately cease and not continue to access the site if you are under the age of 18.
>>7694715
his idea is dogshit. defining 1 to be something that can construct 3 thus proving the existence of 1 and 3 wouldnt fly even in your phil 101 class
>>7694724
>the other is asking if squares exist to prove that 3 exists.
He's claiming that 3 exists because you can construct it. The other guy is saying he can't.
Squares can also be constructed but perfect squares do not exist in the real world. So do squares exist or not?
>>7694601
Don't take classes from Wildberger.
>>7694731
I never said that it proved the existence of 1.
As I said, the ancient mathematicians (who came up with what I am telling you right now) did not think of 1 as a number because of this. It was not a number, it was the building block of numbers like 3.
Then, when we abstracted our numbers, we started calling 1 a number too.
based wildberger
>>7694714
4 is a property that designates the sides of a square
a property of an object is objective if the object is objective
so the number 4 is objective as a property of an object, and as 4 is classified as a real number real numbers exist
>>7694745
I see what you are trying to say and you are failing horribly at it.
My argument for "3" existing does not translate to real numbers existing. Wanna know why?
Because the classification of real numbers came way after the idea of numbers were abstracted out of geometry.
You can construct 3. You can construct various real numbers. You cannot construct all of the real numbers. (I already mentioned how the geometrical definition became outdated when irrationals came along)
Anyways, prove to me that you cannot construct the number 3 and I will proudly say:
You are fucking retarded for not being able to grasp an idea 2500 years old.
>>7694601
He's right but who gives a heck?
>>7694601
This question is very badly defined.
What is our universe of discourse here?
take a 3 which =3 in set lR. define lR to be real numbers, which exist. therefore, 3 is a real, existing number
qed
>>7694601
The discussion about "3" made me remember about a high school geometry textbook I read back in the day. To help that guy out I will tell you this: The introduction of the book started by saying that various things like points and lines are not rigorously defined and they are just accepted and used because they are the tools we use to make theorems.
In other words: A handful of people in this thread can't into high school geometry.
>>7694794
>the real numbers are called real because they're not p-adic numbers
>the real numbers are called real because they're not birthday cake numbers
>the real numbers are called real because they're not bank account numbers
Maybe he has asbergers or something. Dont worry about it.
>>7694766
like I said before the professor is trolling
real numbers are called real because they are not imaginary numbers or complex numbers
a small amount of real numbers exist, the rest can't be defined as a property of anything as they are irrational. the professor saying all real numbers don't exist is false
>>7694801
https://en.wikipedia.org/wiki/Real_number
https://en.wikipedia.org/wiki/Imaginary_number
>>7694820
And your point by linking those is what?
>>7694820
Oh boy this kid.
>http://www.4chan.org/rules
>You will immediately cease and not continue to access the site if you are under the age of 18.
underaged & b&
If 3 doesnt exist, how does the San Bernandino shooing exist?
>>7694887
did 3 ppl die? or did ppl die and there were 3? pretty profound stuff itt
>>7694914
>https://en.wikipedia.org/wiki/Suicide
>https://en.wikipedia.org/wiki/Seppuku
>https://en.wikipedia.org/wiki/Sudoku
>>7694941
Supposedly, 3 shooters.
>>7694662
But one pinecone = 100s of billions of atoms. One pinecone = 1/x of a tree.
>>7694887
My dick obviously.
Obviously he was trolling. Look at the shit show he stirred among the idiots above /\
>>7694956
>Oh boy this kid.
>>7694962
But this is mathematics.
You could define your unit to be an atom. Or you could define your unit to be a pinecone. It works either way. You just keep working on your scale.
Then physics came along and we convert meters to centimeters, atoms to pinecones, etc.
But in mathematics it doesn't matter.
To prove, say, pythgoras' theorem we just need to define a triangle of x units. It doesn't matter what x is or what the unit is. Mathematics works regardless.
>>7695000
underage
>>7694796
Made a 7 in geometry.
Lotta underage b& in this thread. Time to give a speech for the babies, I suppose.
Numbers themselves don't exist. They are abstract concepts that we denote with symbols in order to determine relationships between abstract concepts that may or may not exist.
Mathematics is the apex of the quantitative hierarchy because it is a language that describes truth, truth which is evident in empirical reality but which is free from concerns like whether or not "reality" exists.
This is, perhaps, why mathematics has been described as the language of God.
Consider this: If the universe itself did not exist, the circumference of a circle with a radius of 0.5 would still be equal to pi.
Circles wouldn't exist, diameters would not exist, units would not exist, quantitative measurements would not exist, language would not exist, an observer to do mathematics would not exist; but the following statement would still be true:
>C=2Ï€r
That relationship, between abstract concepts, is true. Regardless of whether or not anything exists or whether or not anything is "real": the relationship, as described, is true.
Perhaps that is what >>7694601's professor meant.
>>7694704
>First, I am not talking about numbers. I am talking about segments. That is how we used to define numbers, until it became an outdated method when we discovered irrational numbers.
Nigga what? The Greeks discovered irrational numbers and kept using geometry to define shit for centuries. Euclid's Elements has a fucking chapter about irrational numbers.
this thread is the result of /sci/'s anti-philosophy culture.
>>7696247
This.
/sci/ can't into metaphysics, which is a separate field than mathematics. To confuse the two is 4chan/reddit tier mistake. If OP wanted to troll he'd have posted
>are axioms real?
>>7694601
Yes, they can be constructed from Q pretty easily, plus you can make them synthetically.
>>7694662
3 exists, it's { { { { } } } }
>>7697188
you some kinda dumb huh?
it's really {{},{{}},{{},{{}}}}
>>7697188
idieet
>>7696247
>>7697171
Enlighten a first-year math student who plans to take no philosophy courses (since I want to take as many math courses as possible).
Any good books you can recommend?
![A_JiQdhCEAAnBIi[1].png](https://i.imgur.com/ZsVjYtD.png "A_JiQdhCEAAnBIi[1].png")
>>7697265
>>7697265
Read Bertrand Russell's Introduction to Western Philosophy, and then read Being and Nothingness because analytics a shit.
>>7694601
No two things are exactly alike therefore you cannot have more than one. However it's highly functional and produces things like rockets so unless you have something better shut up and be thankful to your ancestors for this beautiful falsity.
>>7697265
>>7697349
You should also study the I Ching.
>>7697353
Is this some kind of /lit/ meme or "should" I actually do it. I wouldn't mind studying it, anyway.
>>7694704
>until it became an outdated method when we discovered irrational numbers.
> I am claiming that you can construct a unit by drawing something.
you're literally retarded, stop posting any time
>>7695741
Oh, you are right. I did not realize that even in high school we are taught algebra. Nope, I must have been high as fuck. We still do addition with line segments and multiplication, division and roots with triangles. You are totally right.
We never realized that geometry was "outdated" so we never invented algebra.
Totally smart guy here. Believe him! Algebra IS SATANIC!
>>7697265
http://www.amazon.com/gp/product/0195155041. You need this book. If you're a math major. It used to be standard material until the new generation of math retards took over. If you're Pure science or major major and you're not minoring or double majoring in philosophy then you have failed in your field.
>>7697405
nigga what are talking about? the system didn't become outdated because of irrationals, who told you that?
Back in 1672, Mathematicians were exploring newly discovered sections of the sea of axioms. They came across two islands containing two distinctly different ecosystems of numbers. The first one they came across was huge and beautiful, but they found whenever they tried to grab the numbers, they disappeared in their hands. The numbers did not really exist, they were just illusions created by the continuity of space around them. Although mathematicians were able to invent convoluted processes to work with this island, this land was harsh and barely-inhabitable. But there was a lot of it.
Next they came to a smaller land. This island was not so grand and beautiful, but here they found an ecosystem of numbers that was far more health and substantial. They could hold these numbers in their hand, they could build things with them, complex structures came easy. There was no convoluted process of manipulating subtle chinks in an abstract properties of the space, they just put numbers together and things happened.
Mathematicians knew that this land would be ravaged by sight-seers and dilettantes who would not respect the fragile ecosystem. But still wanted to get paid. So they named the island of make-believe numbers that evaporate in your hand "the Real Numbers" and they named the island of tangible numbers that you can actually do things with "the Shitty Fake Numbers" to deter tourists.
And now you know the story.
>>7694720
>Once we have proven or disproven the existence of real numbers in the physical sense, what have we learnt?
>Nothing, absolutely nothing of use.
The fact that such a proof is possible would be pretty interesting at least.
>>7697265
This whole thread is basically
>http://plato.stanford.edu/entries/formalism-mathematics/
vs
>http://plato.stanford.edu/entries/platonism-mathematics/
>>7697512
>Platonism vs Formalism
But both of those are retarded. They are so extreme on the side of interpretation that they both practically say the same thing and it's still nonsense.
>>7697522
>they both practically say the same thing
How do you figure?
Anyway I think these 2 are just the main camps that come in many different varieties. In the end mathematics either really exists or doesn't, in some sense, whatever that means.
If you were to define a number as a root to a set of equations, then real numbers are just as real as imaginary numbers. I honestly don't get what people say when they say real/imaginary numbers don't exist. Both are just as "real" as each other. The real numbers are the set of numbers to which every equation that contains that real root has the implication that x^2 => 0, while with the set of imaginary numbers the inverse implication must be true for every equation that has that imaginary number as a root. That's literally the only difference between them.
My point is that when it comes down to it, numbers are just representations. To say that numbers themselves exist or don't exist is stupid, but you could debate the existence of what they represent. They exist just as much as the word "chair" or "table" exists- they're words that represent something. This isn't even a mathematical question, but a pure philosophic one. What your professor essentially saying is, "representations don't exist."
Sorry for rambling on with my uneducated opinions but there it is
>>7694601
I think he's saying that in a rhetorical way, it's like some sort of paronomasia or something, using the double meaning of "real number", to get a contradiction, but in my humble opinion it's just a catchy phrase, that should not be taken too serious.
Saludos
>Lotta underage b& in this thread.
>If the universe itself did not exist, the circumference of a circle with a radius of 0.5 would still be equal to pi.
Kill yourself.
Technically he is correct. Real numbers are perfect numbers. Great for finance, but irl, numbers and values are always changing. Its why constants are so important.
