Tfw Veeky Forums is always wrong

How long have you been on Veeky Forums? He's a pretty commonplace meme

Not long admittedly

Infinite sets aren't even mathematics. They're pseudo-philosophical woo, and the fact that so many mathematicians cling to them proves that they're just as irrationally dogmatic as religious people and postmodernists.

Provide a counterexample where the definition of the reals and the operations defined on them cause contradictions/unclear statements that are not meme answers which have good rebuttals such as 0.999...=1 or stuff such as 1/0 or 1/infinity not being defined

Well he does have a PhD from Yale and he *is* a professor so I'm guessing at some point he knew his shit. Besides, if you disregard his constant rambling about the reals, his lectures are pretty good.
Something must have happened to him along the way.

The sum of two rationals can always be expressed as another rational, e.g. -4 + 1/2 = -3.5. This is not, however, the case for reals. It's not clear what pi + e, for example, is supposed to mean, beyond just pi + e. This is an example of an unclear statement. You can of course analyze this computationally in terms of algorithms for generating pi and e, but that's vastly more complicated and not generalizable to all reals (or even all computables).

Also, there's nothing wrong with 0.999...=1, or algebraic structures where 1/0 and 1/infinity are defined (e.g. Riemann sphere)

>They're pseudo-philosophical woo
just like finite sets, just like any maths, just like any concept

5.85987448205...

Infinity isn't an element of the reals.

There are plenty of basic arithmetic operations with the reals that are undefined within R .

Arithmetic and the reals are well defined and rigorous.

Meme.

>...
HAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHA

>>Arithmetic and the reals are well defined and rigorous.
arithmetic with reals are not even well defined with dedkind cuts fooking undergrad

0/10

>On a bus
>Some fucking nutjob starts talking to be about "real numbers"
>I say "How can numbers be real if our eyes aren't real" and blew his fucking mind
>Go on Veeky Forums and post this

>5.85987448205...
can you say what's in the dots? You can't, because you would have to know all the digits, then start adding from the end to see if there are any carry before writing anything.

So in conclusion you basically can write almost nothing of this pi+e "number".

Wildberger does a better job at explaining it than I do though.

>It's not clear what pi + e, for example, is supposed to mean
of course it is. replace pi and e with a sequence of rationals (always exists) converging towards them and pi + e will obviously be the limit of the combined sequence.

>This is an example of an unclear statement
maybe...to a brainlet

>too much of a brainlet to understand why it's not rigorous

the irony

then explain it to me...challenge: no handwaving~!

ok good.

Now how can you determine a sequence of rationals for any arbitrary real number?

You can't.

So you can't add two arbitrary "real numbers".

Pi and e are nice sequences, because they're actual sequences.

...

challenge: no handwaving~!

one can construct an arbitrary real (irrational with high probability) number by generating successive digits via a random number generator

>Pi and e are nice sequences
they are constance, not sequences

>one can construct an arbitrary real (irrational with high probability) number by generating successive digits via a random number generator

You're dodging the question.

Let r and s be two real numbers. Give me a finite algorithm to determine a sequence I can use for r and for s so that I can add them up.

they're sequences of rationals.

By definition every real number is an equivalence class of sequences of rationals.

>Give me a finite algorithm to determine a sequence I can use for r and for s so that I can add them up.
sum the successive rational approximations of r and s

clarify what you mean by finite algorithm anyway

good goy

How am I given r and s if not as sequences already? Your question is assuming I have some other representation. What is it?

they're just some *handwave* '''''ARBITRARY''''' real numbers

there's the issue.

oh now we can't use arbitrary numbers? So you do agree with me.

Great discussion boiz.

>there's the issue.
well no. the thing i smell is that you dont like numbers that cannot be represented by n/m.

The same argument can be used to say we can't define addition on the naturals.

>oh now we can't use arbitrary numbers? So you do agree with me.
i don't agree with you. i was trying to allude to your inability to grasp what is meant by `arbitrary real number' because you already don't understand what a real number is

but I do, you don't.

please lay out your argument

There is nothing to like or dislike desu, there are only ideas that can be discussed and arguments that can be convincing or not.

>please lay out your argument
select two arbitrary natural numbers n and m

what exactly is their sum?
n + m?
m + n?

see: it's meaningless!

>Muh formal systems and ordinals

Youre the meme shit, watch a few more videos and you will realize he has pioneered better methods for trigonometry, non euclidean geometry, math foundations, and the calculus of rates of change, separate from analysis enteriely.

On terms purely of an arbitrary theory that can predict and model reality, you can even accept a lot of his methods and still retain a faith in reals numbers and youd still be far ahead of any comprehension you had before.

Wow, I if were defining a number system I would make sure an any number had a canonical representation that would facilitate performing arithmetic operations with it. Too bad the idiots who came up with modern math didn't think of that.

perform arithmetic on any of the rational approximations if you want a ''''number''''
anyway, what does n+m really mean anyway? if we knew what n and m were, it would be easy...you know like n=2,m=5 then n+m=5 but we don't know so its meaningless!

>I'll just pretend to be retarded so I can dodge the issue

count n items, put them together
count m items, put them together with the first n items

now count how many items you have.

Now do that with two arbitrary reals if you can.

Oh wait you can't.

>What are non standard models of arithmetic

As already mentioned in this thread, it is easy to give an algorithm to compute the sum of two arbitrarily given real numbers in some fixed representation. It's retarded to demand anything more. I mean, how do you suppose a real number is given if not in some representation?

Also, if PA is consistent then so is arithmetic on R.

Boys believe in the reals.

Men believe in Wildberger.

I didn't watch the videos.
This is a pythagorean discussion aka "2500 years ago"-discussion. Let's forget about modern, axiomatic math and IR for the moment, what comes immediately to the mind :
What does he say to:
1. What is the ratio between the circumference and the diameter of a cricle?
2. If I draw a square with side length 1m, how long is the diagonal?

im not him.

you realize youre talking about the rationals right? when he says abritrary real number he means an irrational one.

1.
youtu.be/lcIbCZR0HbU?t=33m2s
for Pi, you can watch for a few seconds

2.
he likes to use the notion of quadrance, basically working with squares of numbers rather than square roots.

1.
I watched exactly 10:00 min.:
So he says that Pi is "problematic" because the "real numbers" are "problematic".
Basically it is just denying evidence, isn't it?
And of course you can't teach high school kids about dedekind numbers and cauchy series, and of course forget about non-euclidean or otherwise sophisticated geometry, I mean, come on. Look at this Veeky Forums-board, people on this board, most claiming to be grads, hardy getting it.
2.
I don't get this. There is a line AC in the square ABCD, how long is it if I measure it?

I tried to watch another video but had to constantly skip a few minutes. He talks a lot but doesn't say anything interesting. I wonder what his target audience is. For people with basic math knowledge (say 1st year STEM uni) he really could speed up and come to the point quicker. For others, he seems to just impress them.

I really try to be open minded to whatever. But this guy did not impress me nor did he raise any doubts about the concepts in question * and I don't think he really knows/understands what he is talking about.

* Besides: Every mathematician knows that IR / the continuum is not a trivial topic.

Nah, to my knowledge wildeburger isn't working with god in the fight against the CIA niggers.

cont.:
*dedekind cuts*

>They're pseudo-philosophical woo
All of math is technically this

Not that guy but even if you accept Graham's number existing on account of it having a small finite description that doesn't mean that you can argue that all the naturals exist.

Some naturals out there can only be explicitly described with descriptions so long that they don't fit in our universe. You will never be able to prove a theorem or give a result specific to that number. At best you could give a result about a set of numbers of which said number is a member even though never explicitly mentioned (eg. the set of all naturals larger than 3).

How can you tell me that a number exists if you can't even demonstrate or describe it? How can you even justify needing it to exist if you can never explicitly write it or prove anything about it? You can't even explicitly concede that such a number doesn't exist, you are pretty much by definition forced to concede that the set of all such numbers doesn't exist and that immediately puts you into the realm of finitism.

No, he's the Troy Hurtubise of Veeky Forums. Terry Davis is just the Troy Hurtubise of /g/.

Troy belongs to /diy/.

that's true, though. as far as we know, the highest number = (the number of quarks in the universe). there can be no more of anything as much as there is of the number of quarks. it's impossible.

>Basically it is just denying evidence, isn't it?
No, that's what he spends hours explaining before.

>And of course you can't teach high school kids about dedekind numbers and cauchy series, and of course forget about non-euclidean or otherwise sophisticated geometry, I mean, come on. Look at this Veeky Forums-board, people on this board, most claiming to be grads, hardy getting it.
Pure math isn't meant to be fun or easy. It's just what it is. And right now it's non rigorous.

Not that guy but your concept of "demonstrating" or "describing" a number is itself a necessarily undefinable concept (by Richard's paradox), and if you can't justify your position then you have no argument against someone who chooses to dismisses it without justification.

it's not even without justification. If an argument is not convincing or produces paradoxes, you can't expect everyone to be convinced.

>
*tip*

>unconscious incompetence

Undefinability occurs at the metamathematical level.

pi+e is between 5.8599 en 5.898
For almost all applications this is precise enough.
The thing is if you define all allowed calculations by computational practicallity you can just add the just as arbitrary convention of rounding numbers within practical error.
All plots you have ever seen of analytical functions are just approximations of that function, within a certain error.
Doesn't mean they don't exist or are not useful

>*between 5.8599 and 5.8598

So you can't do statistical mechanics than. There are more permutations of all quarks in the universe than there are quarks in the universe.

there are lots of abusive things in physics.

this one is probably the worst offender en.wikipedia.org/wiki/Renormalization

Rational trigonometry is beautiful
Death to linearized angle measurements.

That's not a rigorous definition though.

> Doesn't mean they don't exist or are not useful
what if I told you, you didn't have to use them though?

Pi + e is the union of the respective dedekind cuts. So what if there's no finite decimal expansion? They're still a perfectly well-defined mathematical object.

what about pi-e? and pi * e?

Those are rational numbers.

How am I going to plot the alternatives?

You should publish your proofs and attain undying fame.

I still got no answer to the simple question: If I have a square with side length 1m, how long is the diagonal?

'Side length' doesn't exist. Did you mean quadrance?
If you have square whose sides have quadrance 1 then the diagonal has quadrance 2.

you had your answer, use quandrance and stop using lengths.

No I'm not

Clearly it must have a length.

maybe it does, but we don't understand lengths very well yet. Mathematicians must work at developing better theories than the current trash that we call "real numbers".

>religious people and postmodernists
>postmodernists
You aren't even be able to define postmodernism. Stop browsing /pol/.

does the length have to be a real number tho

t. engineer

>>Clearly it must have a length.
then prove it

pythagoras: the length is [math]\sqrt{2}[/math]

thats what computer science is for

So all "[math]\sqrt2[/math]" implies is that it has another similar part which when combined together equals "2". Care to give me a precise amount to how much that magical part is?

I'll keep real numbers thanks... they allow me to do interesting mathematics, meanwhile you ultrafinitists can keep on doing your "exciting" rational trigonometry.

( sqrt 2 )^2
desu

Is atleast his Math History series good?

Nominalist? On MY Veeky Forums?
Unless you're ante rem/in re structuralist, in which case you're kinda alright.

What if we assign the number 2 to each quark rather than just 1?

Now we have represented the number 2N where N is the number of quarks.

Renormalization is only abusive if you pretend the models it's used in are supposed to be theories of everything. Otherwise it's just a fact.

What's the quadrance of AB in pic related?

Pythagoras says you're wrong though.

They are. Or instead of Dedekind cuts we can define reals as limits of Cauchy series of rationals, and then addition and multiplication of reals will be just addition and multiplication of sequences of rationals, and I don't think you'll say arithmetic with rationals is not well defined

I thought Wildburder was a venison restaurant? Veeky Forums lied to me again goddammit.