Mathematical misconceptions

Every invite string that has a chance to contain a substring does contain thus substring. Pi is (as far as we know) random. Random means that there is after every character a equal chance for ever possible next character.
Your example isn't random it still contains every substring possible.
Sage

And here, ladies and gents, we have just what OP was talking about.
Up next: How many Veeky Forumsentists will insist that the universe is deterministic, even though we've know it isn't for nearly a century?

> a mathematical constant is random
8[

Sounds like you should publish your results d4wg, seems pretty ground-breaking.

Check out this post about misconceptions in probability theory

>I think "normal numbers" means random
Epic

>Pi is a normal number
Proof ?

Why would anyone assume that? Mathematics doesnt work like that, because an example is not a proof.
Even if it were actually repeating, as long as we cant proof that its repeating its meaningless.

and in fact we can prove that it's NOT repeating, because it's irrational. (It's actually more, it's Transcendental, but proving irrationality or transcendence of pi are not incredibly easy)

> video games with square world maps take place on a sphere

If the top wraps around to the bottom, and the left wraps around to the right, then you're probably looking at a Torus.

Still waiting for a video game with a non-orientable world map

totaly agree.
Sometime I wish there are video game wich take place on a projective plan.

Aren't there some arcade versions of Asteroids where you play on a disk and when you reach the boundary you come back in at the antipodal point?

>pi is random

jesus fucking christ...

wouldn't that still be a torus, only with the radius in the center of the torus being zero?

I've only seen Asteroids on a torus, but now I'm motivated to write one that takes place on RP^2.

Just in case you don't know, remember that you can do it whit a disk or a square.

nop.

Not specifically math, but highly related:
> A implies B
> not A
> Therefore not B

This is obviously invalid, but people still do this all of the time. I TA'd an "Intro to Mathematical Logic" course once and it hurt my feels every time someone did this because it meant that I'd failed them.

Also not non-elementary

>For every statement you can either find a proof or a counterexample

>Pi can only contain all infinite strings that do not repeat.
>such as 3487490123127654...

Is this true?

yes i could

Like how you can't disprove a "there exists" statement with a counter-example

troll

That would mean intuitionistic logic is the same as classical logic. Are there people out there actually believing this?

John Nash was a tragic hero who overcame his crippling autism to save America from the Cold War.

>[math]\sum{n \,=\, 0}^\infty n \,=\, -\frac{1}{12}[/math]

It's true that's pi's decimal expansion is non-repeating.

What do you mean precisely by "contain"?

So does dy/dx mean that dy is divided by dx?

I like how I just learned about Leibniz notation last week and can now laugh at this.

"almost all"**

Most don't understand that something can be undecidable.

How exactly do you define "non-repeating"? I'd define it as not being able to find an identical sequence of digits in the string from the beginning up till the point where you find the repeat, but in that case your string clearly repeats itself in the first four digits (1010).

almost all what? almost all strings? no, the string
1010010001000010000010000001...
contains almost no strings in {0,...,9}*

What I'm getting out of this thread is drugs are bad.

Spoken like a true layperson.

>Counter-example: The binary string
>'1010010001000010000010000001......'
>is infinite and non-repeating, but it doesn't contain the finite string '11'.
but it's not random.

Ooh I know this one: Goerdel's Completeness Theorem.

:^)

As already said: there is no proof that pi is random or not.

A sequence is "repeating" if after a certain point it is just a finite string repeated indefinitely.

A sequence is "non-repeating" if it is not repeating.

OP didn't say a single god-damn thing about randomness.

Also, check out this post about misconceptions in probability theory:

As already said, the statement "pi is random" literally doesn't make sense. It's not just false: mathematical constants aren't even in the realm of things to which the adjective "random" applies.

He didn't have autism, he had schizophrenia.

>John Nash was a tragic hero who overcame his crippling autism to save America from the Cold War.

he was however a schizo who saved us from the CIA

It's possible that they meant "almost all infinite sequences are disjunctive".
(a sequence is a language is called "disjunctive" if it contains every finite string in that language; let's say a number is "disjunctive" if its decimal expansion is a disjunctive sequence)

This statement is actually true, (once you clarify what "almost all" means in the sense of measure theory and specify which measure is being used on the set of all infinite sequences), and it's the correct caveat to make to OP's misconception. The problem is that most people don't realize that this caveat is needed, because they think "Probability 1" means "in all cases" and not just "in almost all cases".

With regards to pi, you can't use a probabilistic approach to the question of whether it's disjunctive or not, because pi is A SPECIFIC NUMBER. That's why we're able to compute its decimal expansion in the first place. The decimal expansion is not a random variable, though it MAY appear to BEHAVE like one. pi could fall inside this Probability 1 subset of disjunctive numbers, or it could be in the non-empty Probability 0 compliment. We literally do not know.

All we can say with certainty at this point is "pi is probably dusjunctive, maybe?"

>100% probability

0, actually

1, actually. This is a result that someone proved and you can look up.

en.wikipedia.org/wiki/Infinite_monkey_theorem

computer model simulation proves it's 0

gr8 b8 m8.

Where can I borrow infinite computing power? I could really use that right now.

•All the sonnets are the same length. They're by definition fourteen lines long. I picked the one I knew the opening line for, "Shall I compare thee to a summer's day?" I counted the number of letters; there are 488 letters in the sonnet. What's the likelihood of hammering away and getting 488 letters in exact sequence as in "Shall I campare thee to a summer's day? What you end up with is 26 multiplied by itself 488 times - or 26 to the 488th power. Or, in other words, in base 10,10 to the 690th.

•Now the number of particles in the universe - not grains of sand, I'm talking about protons, electrons, and neutrons - is 10 to the 80th . Ten to the 80th is 1 with 80 zeros after it. Ten to 690th is 1 with 690 zeros after it. There are not enough particles in the universe to write down the trials; you'd be off by a factor of 10 to the 600th.

•If you took the entire universe and converted it to computer chips - forget the monkeys - each one weighing a millionth of a gram and had each computer chip able to spin out 288 trials at, say, a million times a second; if you turn the entire universe into these microcomputer chips and these chips were spinning a million times a second (producing) random letters, the number of trials you would get since the beginning of time would be 10 to the 90th trials. It would be off again by a factor of 10 to the 600th. You will never get a sonnet by chance. The universe would have to be 10 to the 600th time larger. Yet the world just thinks monkeys can do it every time.

>Yet the world just thinks monkeys can do it every time.

1) These aren't monkeys. These are INFINITE monkeys. You're maybe not appreciating just how much bigger infinite things are than finite things. Like, by definition, bigger than any finite thing.
2) Ok, again: "Probability 1" doesn't mean "Every time."

>Now the number of particles in the universe
Mathematics doesn't concern itself with the physical universe.
>Yet the world just thinks monkeys can do it every time.
It's just a metaphor you autist. "infinite random string of letters theorem" wouldn't sound as catchy.

>the universe isn't deterministic

>there exists a rigorous mathematical proof of a statement concerning an infinite probability space
>but checking finitely many things is more valid

This wouldn't be a math thread unless somebody was complaining about a metaphor used to describe math they don't understand.

More or less, but not exactly.

>then there is a 100% probability that they will write every finite string
isnt it that the limit of the probability is 1 at infinity ?. if what arey are writing is truly random (equally likely to type any character) that is .
its the same with le wavefunction, the entire universe is located on my dick , just with pretty low probability .

its correct if you make the assumption that the base the digits of pi are truly random , that is all digits are equally likely when calculating the next one , which i think is true for the known subset of the digital representation of pi.
but this dosnt make sense since pi isnt 'random' its determined by the geometry of the universe .

it has been experimentally proven u kek

cant decide if the mistake is that "factor" should be "multiple"
or if 28 and 7 need to be switched

>linguistic-world problems

>experimentally

We are talking about Maths

Is confusing factor and multiple a real problem for people?

I have the most basic of white American educations and knew nothing about math, but I wouldn't do that.

>Is confusing factor and multiple a real problem for people?
youre mistaken
people just mix 28 and 7 up alot

I think it's genetic, you must not have the gene

...

>isnt it that the limit of the probability is 1 at infinity ?
Yes.
As the length of a random string approaches infinity, the probability that every finite string appears within it approaches 1. But, also yes, it's just a probabilistic statement and it's entirely possible that if you pick an infinite string at random it just says "fuck you" infinitely many times: if it's truly random then ANY possibility should be plausible. If you say something has "100% probability" that doesn't mean it definitely happens, it just means it "almost always" happens.

> its correct if you make the assumption that the base the digits of pi are truly random
you can also prove everything if you assume x is not x

>but this dosnt make sense since pi isnt 'random'
Absolutely correct. It doesn't make sense to talk about a constant as if it's random.

By the digits of pi being "random" I think what you really mean is whether pi is a "normal" number or not, i.e. the digits show up in a roughly uniform distribution. Here's a small thing that talks about normality, and about whether pi in particular is maybe normal: pi314.at/math/normal.html

That happened. About 200 (I think) digits in, we got the string ... 99999

And it was thought that it was just 9s from there, so they stopped calculating.

This was before modern understanding of analysis, obviously.

I dunno, I just googled "math misconceptions" and tried to find the catchiest photo, and one which depicted horror at a concept so rudimentary just seemed the most appropriate.

Classic Mistake, Milhouse. Classic Mistake.

>believing [math]i \hbar \frac{\partial \Psi}{\partial t} = \hat H \Psi [/math] isn't deterministic.

>believing that the wave form of a quantum system determines observations.

Who the fuck believes this?

This is the most common fallacy to exist probably.

If you commit this fallacy in real life, it's often not a big deal. If you commit this fallacy in math, you should probably kill yourself.

You're using irony?

The definition of a normal number simply corresponds to the frequentist interpretation of probability. While you are right in that every constant is either nornal or not, your BELIEF that it is random can be equipped with a probability measure under the Bayesian interpretation. In particular, if I have zero background knowledge to decide either for or against the proposition, then there is literally nothing wrong with me saying that the probability is 50-50.
This is because the probability is a measure of my belief in the proposition and has mothing to do with the proposition itself. Mathematically, a probability is nothing but a function from a collection of sets to [0,1], and it 'exists' insofar as the ground set is well-specified.

>The binary string
>'1010010001000010000010000001......'
>is infinite and non-repeating, but it doesn't contain the finite string '11'.
Did you check all of it, smarty-pants? Maybe it does if you go all the way to the end.

>>>Your Honor, this man claimed UNDER OATH to be certain that a sequence of digits didn't contain a certain substring, but in truth he didn't in fact check all of the numbers all the way to the end himself.
>>Is this true?
>Yes, Your Honor, but...
>>Silence! Order in the court! You are hereby found in contempt of basic common sense! I sentence you to pound-you-in-the-ass prison! Guard, take this man out of my sight! We are done with his testimony!

Hope it was worth it, Smartso the Brainiacal Wizard.

He's completely correct. You need at least seven nines after the decimal point for it to be equal to one.

The whole "Infinite random input mapped to alphabetical output has every string of words possible" is just a fancy way of saying that an abecedary can be arranged to say everything in our language.

You have absolutely no Idea what you are talking about OP VERY clearly proved that a non repeating string of 1s and 0s exists that does not contain any substring.

If you cant grasp that simple concept you should really leave this board because you clearly have no Idea about maths even on a high school level.

>at least seven nines
such precision is not possible in the physical universe

String Theory

but you can define

00 to be 0
01 to be 0
10 to be 1
11 to be 1

and now you can find the string 11 :)

the pattern is there

1=1
define 1=2
1=/=1
therefore maths is wrong

That is the shit you are doing.Of course you can redefine shit but you end up with a different string of characters or a straight up contradiction.

You are a dumb shit m8

If you have an axiom that says 1=2, then 1=2, and therefore 1=1 is still true

are you retarded?
In mathematics there is a concept of something being "well defined" meaning that it is not a contradiction and is consistent with the rest of mathematics.

Saying "define 1=2" is ill defined meaning that it is inconsistent and therefore not valid.

But what you did was even dumber you just redefined things to get a DIFFERENT series. Which makes absolutely no sense because OP without a sliver of doubt proved that a non repeating series exists that does not contain every possible sub series.
What you did was to prove that a series exists which contains the string 11.

>and therefore 1=1 is still true
Assuming x=x is an axiom.

>he thinks that math is anything but the logical conclusions that derive from a set of axioms
>he thinks you can't add a new axiom and derive more conclusions without it being contradictory

>he thinks you can't define two categories, one that includes a pair of elements, another that includes another pair of elements
>he doesn't know that patterns can include subpatterns, and all subpatterns are part of the pattern

brainlets these days

>he thinks that math is anything but the logical conclusions that derive from a set of axioms
I dont
>he thinks you can't add a new axiom and derive more conclusions without it being contradictory
i dont

Lets try this again:
You have a set of axioms from them you derive something. Then you define something to be a contradiction to these axioms and what you have derived from them.
That is called "ill defined".

>he thinks you can't define two categories, one that includes a pair of elements, another that includes another pair of elements
I dont
>he doesn't know that patterns can include subpatterns, and all subpatterns are part of the pattern
I dont
Have you still not understood that defining a new series means that it is DIFFERENT I though that was basic common sense.
OP proved that a series exists that does not contain the sub series "11" you proved by construction that a series that does.

[citation needed]

not him but
geom.uiuc.edu/~huberty/math5337/groupe/digits.html
ctrl f for 999999
or here
angio.net/pi/digits.html
even 99999999 is included in pi

Does the infinite string of Pi contain every possible integer represented as a finite string of digits.

No one knows. And proving it seems not very easy.

Redefine the string to just say "fuck you" infinitely many times. Now there is a pattern.

You forgot to mention that 2 =/= 1 by the Axiom of Extensionality (the one which says two sets are equal if and only if they have the same elements).

However, adding the assumption "1=2" doesn't mean "maths is wrong". You can always add axioms to formal systems to produce new formal systems. The point is that you've produced a NEW formal system with new rules, and this new formal system may not be consistent anymore, i.e. you might be able to derive a contradiction. If you can derive a contradiction then you can actually prove EVERY statement (true AND false) so the resulting formal system is utterly useless, and the added assumption was a v bad assumption indeed.

The takeaway is that is you want to prove A=>B, and you've proven (A and C)=>B, then you haven't really accomplished what you set out to do. If you've ACTUALLY proven that (A and B)=>B then you might consider killing yourself.

x=x actually follows from the Axiom of Extensionality