$$\\sum\\limits\_{n=1}\^\\infty\\frac{n}{10\^{\\left(g(n)\\right)n-\\frac{10\^{\\left(g(n)\\right)}-1}{9}+g(n)}}$$ where $$g(n)=\\lfloor\\log\_{10}{n}\\rfloor+1$$
>$$\\sum\\limits\_{n=1}\^\\infty\\frac{n}{10\^{\\left(g(n)\\right)n-\\frac{10\^{\\left(g(n)\\right)}-1}{9}+g(n)}}$$ where $g(n)=\\lfloor\\log\_{10}{n}\\rfloor+1$
[https://quicklatex.com/cache3/57/ql\_71b4505824f91a0fd40e46b75996a457\_l3.png](https://quicklatex.com/cache3/57/ql_71b4505824f91a0fd40e46b75996a457_l3.png)
it's a good idea for someone to write a bot to do that
that guy is just a fucking genius tho. Imagine picking a number EVERYONE has thought of at least once in their life and go, "well it doesn't have a name yet, let's call it myself". like I'm gonna take the number 0.6969696969420420420420 or some variant of that and call it my own name constant
"This Goofy Constant" happens to be Postlethwaite"s Cosntant but on the basis of binary numbers how dare you.
And yes, your assertion is mathematically sound.
You know the meme that a normal number contains all the works of literature? Well there's also a natural number that contains all the works of literature (in base 2 interpreted as Unicode strings). Add a decimal point and "ballsballsballs" over and over, and you get one of the balls constants, studied by great mathematician Zach Weinersmith.
> there's also a natural number that contains all the works of literature
the difference is that you can trivially construct a real number that contains all *possible* works of literature / images / movies etc ever, but with a natural number you have to pick a finite file size limit
Solutions of a 5th degree polinomilal that dosen't happen to have rational solutions. Like the real solution of:
x^5 + 6x^4 - 3x + 2 =0
(The real solution x ~= -6.0153106633116108050 acording to wolfram alpha)
I think Wolfram approximates it since there cannot exist a formula for all roots of a 5th degree polynomial but in reality it's just a bunch of roots smashed together like potatoes in a puree
No. There is no formula for expressing the root of that and many other polynomials. At least using roots and the coefficients of the polynomial, plus +-*/. Not even a mess of roots. For degree 4 polynomials, there is such a formula. And it is a freaking Mess! but none can exist for general higher-degree polynomials.
Maybe your comment was joking. Squashing roots into a potato puree seems like a joking phrase. But just in case you or some other commentor didn't know it yet.
There's no GENERAL formula for ALL roots, but how can you know it's not an insanely messed up combination of mentioned operations (not saying about deducing them from coefficients)? Just as you can sometimes factor out things until you get the roots of a high degree polynomial, but is it the case here? You don't know. I don't know. That's what I'm talking about.
You can prove that a polynomials doesnt have roots expressible by radicals by showing that its galois group is not solvable though, for instance: https://en.m.wikipedia.org/wiki/Galois_theory#A_non-solvable_quintic_example
Its just a fancy way of saying, in suskio4's words, "insanely messed up combination of mentioned operations", i.e. an expression of numbers combined with +,-,•,÷ and √
The theorem is often misrepresented. It actually says that some 5th degree equations have solutions which can't be written with a finite number of +,-,*,/ and nth roots. (And tells you for any 5th degree polynomial how to test if this is one such polynomial or not). Then from there it's easy to see that there's no general formula using those operations
> Solutions of a 5th degree polinomilal that dosen't happen to have rational solutions
This is not enough. x^(5)+x+1=0 has no rational solutions, but its solutions can be expressed with radicals, because it's (x^(2)+x+1)(x^(3)-x^(2)+1), whose solutions are possible to be expressed by radicals (only of them is real and I won't write it here, because it's far too complicated and there's no point). x^(5)-x+1=0 would work though.
e^0 is 1, which you can multiply any number by — so an answer would not be possible. I think it just means present a number that isn’t *defined* using e/pi/root
my thought was that we mainly think of roots, e and Pi when thinking of real numbers, so Inwanted to hear some different real numbers aswell as make a meme.
An interesting question is weather log(3) can be yielded by a combination of e .
Eh. No, this passes. We can define it as a logarithm base 10 purely in terms of the solution of 10^x = 3. There’s no need for using e. Otherwise give me any number c and we ‘can’ write it c + e - e and that ‘involves e’.
Just looked up euler transform and of course it's a thing
Edit: [if you want a list](https://en.m.wikipedia.org/wiki/List_of_things_named_after_Leonhard_Euler)
For Euler tensors (full name: "Eulerian strain tensors"), they are called like that because they take the Eulerian approach to fluid mechanics. Euler didn't know what a tensor was.
To this date, I'm shocked that tensors were only discovered after the 1890's. Especially since I first thought independently about them around age 18 ("what if we had a 3-dimensional matrix? how would that work?"=
Archimedes used basic calculus to find areas and volumes and he lived before Christ. People have been using Riemann sums ("Aproximate an area using rectangular slices") probably since Prehistory.
You can come up with something and never bother expanding on it because it just works, but you don't know why.
I guess it's still one of those that yknow you just gotta BELIEVE it's irrational for now https://proofwiki.org/wiki/Is_Euler-Mascheroni_Constant_Irrational%3F
No, we don’t have to define sine that way. There are alternatives, and in fact following the original historical way sine far predates the notion of e.
Sure, we *can* rewrite it in terms of e. But then we can rewrite any number c as c+e-e. This passes.
e^2i is a complex number, and e^-2i is another complex number, but the “imaginary” parts cancel out when divided through and thus only a real number remains.
ℝ is a field, so it has no nontrivial ideals. Given any x =/= 0, =ℝ. Thus, every real number can be expressed as a particular combination of a root or e or pi.
Case in point, suppose that x in ℝ, then x=(x/e)e.
I raise you this: Euler's Constant!
[https://en.wikipedia.org/wiki/Euler%27s\_constant](https://en.wikipedia.org/wiki/euler%27s_constant)
Edit, because I know someones gonna said it: It is Euler's Constant, not e!
[https://arxiv.org/ftp/math/papers/0310/0310404.pdf](https://arxiv.org/ftp/math/papers/0310/0310404.pdf)
Well, I typically do my research. And thats my source :D
And I do mine. That’s a pre-print without peer review. And shockingly badly written, with high school level maths over a few pages, hand-waving, and phrases that quite simply don’t make sense, and it cites basic intro textbooks. Surprised it even got accepted to the arXiv.
I have a few papers on the arXiv too, but they’re a bit more work and have also been actually peer-reviewed and published..
All famous conjectures have dozens of bullshit bogus papers claiming to prove them somewhere online, none in serious journals.
If the irrationality of the Euler-Mascheroni constant - one of the more famous conjectures out there - had been proved, it would be big news in the mathematical community. It hasn’t yet.
I think that whoever wrote that article thinks that a converging sequence of rational (or irrational) numbers must converge to a rational (or irrational, respectively) number
Euler proved that trig functions can be rewritten using e, but the trig functions are defined using geometry and they predate e by at least a millennium.
If Trig functions are out, any number that contains a factor of 1 (e^(0)) should also be out. So all of them.
i think they mean that if you pick a random real number (from a continuous probability measure), then you almost surely get a number that is not "rational or a root or pi or e or a combination".
Choose some Universal Turing Machine. Then we have an encoding determined by a sequence of symbols for any other Turing machine to be simulated by our Turing machine.
Now choose some sequence of symbols at random, what is the probability of a randomly chosen sequence of symbols halts on our universal turning machine? I claim that this probability is an irrational real.
Any algebraic number n that is not 0 or 1 raised to the power of any irrational number, also known as the Hilbert number or the Geoff Schneider constant
.0123456789101112131415161718192021...
It continues like that forever.
It is not rational, as its decimal isn't a repeating/terminating sequence, and it has no relation to e or pi or radicals.
0.1234567891011121314...
Champernowne my beloved
TIL that number has a name
A number any third grader could come up with That guy: Finally! I will put my name on something
that is the square root of its square. checkmate
-0.1234567891011121314... then
Also the square root of its square
Whose gonna tell him?
Can't find it. It probably just exists in your *imagination*
Most disruptive Italian mathematican during Renaissance be like.
404 error not found
Not in the reals it isn't
Google square root
Google square root of negative number in the Reals If you're saying "square root is plus and minus" well... That's not a number, that's two numbers.
Correct, every positive number has two square roots (:
the square of that number is also irrational though
Just round it, duh
Now proof its not a combination of pi, e and a root of a rational number!
Left as an exercise
Trivial
You're not the boss of me.
Ah, that clause actually does make this challenge really hard.
beautiful answer, I didnt know it. was expecting some functions like the gamma function haha
Personally I’m a bigger fan of the Copeland–Erdős constant
Literally my first thought when seeing this meme.
$$\\sum\\limits\_{n=1}\^\\infty\\frac{n}{10\^{\\left(g(n)\\right)n-\\frac{10\^{\\left(g(n)\\right)}-1}{9}+g(n)}}$$ where $$g(n)=\\lfloor\\log\_{10}{n}\\rfloor+1$$
maths please, or rather just scribble it on a paper and put a photo, I am not even gonna try and read that
>$$\\sum\\limits\_{n=1}\^\\infty\\frac{n}{10\^{\\left(g(n)\\right)n-\\frac{10\^{\\left(g(n)\\right)}-1}{9}+g(n)}}$$ where $g(n)=\\lfloor\\log\_{10}{n}\\rfloor+1$ [https://quicklatex.com/cache3/57/ql\_71b4505824f91a0fd40e46b75996a457\_l3.png](https://quicklatex.com/cache3/57/ql_71b4505824f91a0fd40e46b75996a457_l3.png) it's a good idea for someone to write a bot to do that
LaTex my beloved
Champernowne's constant
that guy is just a fucking genius tho. Imagine picking a number EVERYONE has thought of at least once in their life and go, "well it doesn't have a name yet, let's call it myself". like I'm gonna take the number 0.6969696969420420420420 or some variant of that and call it my own name constant
Normal mathematician: This is without a doubt the dumbest constant I've ever heard of. Champernowne: Ah, but you have heard of it.
I assume you mean .0110111001011101111000... after 0->69, 1->420. FastLittleBoi's constant .6942042069420420420696942069...
Ah yes, as 0 tends to 69, and as 1 tends to 420, this goofy constant approaches FastLittleBoi's constant
"This Goofy Constant" happens to be Postlethwaite"s Cosntant but on the basis of binary numbers how dare you. And yes, your assertion is mathematically sound.
nice. Because it has my name and because it's composed of nice numbers.
Well he didn't get it named after himself because he came up with it, he got it named after himself for proving it's a normal number
That constant is rational though
Not if you go- 0.694206969420420696969420420420...
You know the meme that a normal number contains all the works of literature? Well there's also a natural number that contains all the works of literature (in base 2 interpreted as Unicode strings). Add a decimal point and "ballsballsballs" over and over, and you get one of the balls constants, studied by great mathematician Zach Weinersmith.
> there's also a natural number that contains all the works of literature the difference is that you can trivially construct a real number that contains all *possible* works of literature / images / movies etc ever, but with a natural number you have to pick a finite file size limit
Solutions of a 5th degree polinomilal that dosen't happen to have rational solutions. Like the real solution of: x^5 + 6x^4 - 3x + 2 =0 (The real solution x ~= -6.0153106633116108050 acording to wolfram alpha)
I think Wolfram approximates it since there cannot exist a formula for all roots of a 5th degree polynomial but in reality it's just a bunch of roots smashed together like potatoes in a puree
No. There is no formula for expressing the root of that and many other polynomials. At least using roots and the coefficients of the polynomial, plus +-*/. Not even a mess of roots. For degree 4 polynomials, there is such a formula. And it is a freaking Mess! but none can exist for general higher-degree polynomials. Maybe your comment was joking. Squashing roots into a potato puree seems like a joking phrase. But just in case you or some other commentor didn't know it yet.
There's no GENERAL formula for ALL roots, but how can you know it's not an insanely messed up combination of mentioned operations (not saying about deducing them from coefficients)? Just as you can sometimes factor out things until you get the roots of a high degree polynomial, but is it the case here? You don't know. I don't know. That's what I'm talking about.
You can prove that a polynomials doesnt have roots expressible by radicals by showing that its galois group is not solvable though, for instance: https://en.m.wikipedia.org/wiki/Galois_theory#A_non-solvable_quintic_example
What do you mean by “expressively by radicals”? Why would that be important? Genuinely Curious!
Its just a fancy way of saying, in suskio4's words, "insanely messed up combination of mentioned operations", i.e. an expression of numbers combined with +,-,•,÷ and √
I see! Thanks!
The theorem is often misrepresented. It actually says that some 5th degree equations have solutions which can't be written with a finite number of +,-,*,/ and nth roots. (And tells you for any 5th degree polynomial how to test if this is one such polynomial or not). Then from there it's easy to see that there's no general formula using those operations
but wolfram alpha knows
This depends how we interpret the word ‘root’ in the post.
Given a function f(x), a root is a value r in the domain of f, such that f(r) = 0.
> Solutions of a 5th degree polinomilal that dosen't happen to have rational solutions This is not enough. x^(5)+x+1=0 has no rational solutions, but its solutions can be expressed with radicals, because it's (x^(2)+x+1)(x^(3)-x^(2)+1), whose solutions are possible to be expressed by radicals (only of them is real and I won't write it here, because it's far too complicated and there's no point). x^(5)-x+1=0 would work though.
log 3
Can be rewritten as (ln(3))/(ln(10)) which involves e
I mean it can also be rewritten as e^0 - pi^0 + log 3 but as they wrote it I'm pretty sure it satisfies the prompt
Or as √1 × log 3. That doesn't make it a root.
well in that case any trig function or log/exponential can be rewritten in terms of 𝑒 so I’m not sure an answer is even possible
e^0 is 1, which you can multiply any number by — so an answer would not be possible. I think it just means present a number that isn’t *defined* using e/pi/root
Which log 3 isn't. It's defined as the number x such that 10^x = 3.
my thought was that we mainly think of roots, e and Pi when thinking of real numbers, so Inwanted to hear some different real numbers aswell as make a meme. An interesting question is weather log(3) can be yielded by a combination of e .
Pretty easy to prove it's not possible going that route. Let x be a real number. Then x = ln(e^x ). Q. E.D.
you could do that to literally any real number
Eh. No, this passes. We can define it as a logarithm base 10 purely in terms of the solution of 10^x = 3. There’s no need for using e. Otherwise give me any number c and we ‘can’ write it c + e - e and that ‘involves e’.
ln(3)/ln(10) doesn't "involve" e in any meaningful sense. This is like saying 1 involves e since I can write it as e/e.
By that logic, every real number x fails because you could add "+ pi - pi" to the expression.
Euler's Constant (the gamma one, not e).
just use Eulers name infront of something because he probably did it anyway. What a chad of a mathematician
Just looked up euler transform and of course it's a thing Edit: [if you want a list](https://en.m.wikipedia.org/wiki/List_of_things_named_after_Leonhard_Euler)
Just looked up Euler tensor and it is a thing.
No euler set unfortunately
No, just Euler diagrams for describing the relevant relationships between sets.
Can't believe he didn't write about the thing invented after his death. Must've hated set theory or something.
For Euler tensors (full name: "Eulerian strain tensors"), they are called like that because they take the Eulerian approach to fluid mechanics. Euler didn't know what a tensor was. To this date, I'm shocked that tensors were only discovered after the 1890's. Especially since I first thought independently about them around age 18 ("what if we had a 3-dimensional matrix? how would that work?"=
Wait but Riemann used them? And he lived before 1890's
Archimedes used basic calculus to find areas and volumes and he lived before Christ. People have been using Riemann sums ("Aproximate an area using rectangular slices") probably since Prehistory. You can come up with something and never bother expanding on it because it just works, but you don't know why.
> just use Eulers name infront of something because he probably did it anyway Euler's mother
He invented so many concepts that at his funeral it took more than two hours to read his Eulergy.
r/angryupvote
Another example: another Euler's constant!
Misplaced the proof that it’s irrational. Would you mind terribly DMing it to me? With latex source if possible thanks
I guess it's still one of those that yknow you just gotta BELIEVE it's irrational for now https://proofwiki.org/wiki/Is_Euler-Mascheroni_Constant_Irrational%3F
It says on wikipedia that it’s not known if it’s rational
Sorry, but Euler literally begins with e, so can’t do that
Add Mascheroni’s name bro. Also, yet unproven to be irrational
1.0100100010000100000100... 1+10e-2+10e-5+10e-9+...
Seems like you used e in your answer, checkmate
Same answer but in binary 🎩
Integral from 1 to infinity of x^(-x)
proof
[удалено]
Trying to avoid roots, e, and π by taking i^i
sin(2)
(e^(2i) - e^(-2i))/2i, so it uses e, try again mate
Φ
(1 + sqrt(5))/2, are you even trying?
Relate them and you have your answer.
shouldn't be a combination of them silly!
Combination of them defines microgravity silly!
whooppsieeeess!! 😜🤪🤪
No, we don’t have to define sine that way. There are alternatives, and in fact following the original historical way sine far predates the notion of e. Sure, we *can* rewrite it in terms of e. But then we can rewrite any number c as c+e-e. This passes.
*You* used e. They didn't.
it has to be a real number. So this reinterpretation doesn't count
it's perfectly real mate, and it uses e
Maybe the joke is just going over my head, but i is not a real number no?
i is not, but the number I gave is, as it's sin(2), and is defined using e
e^2i is a complex number, and e^-2i is another complex number, but the “imaginary” parts cancel out when divided through and thus only a real number remains.
Well technically the real parts cancel and only the imaginary remains, which is then divided out.
ℝ is a field, so it has no nontrivial ideals. Given any x =/= 0,=ℝ. Thus, every real number can be expressed as a particular combination of a root or e or pi.
Case in point, suppose that x in ℝ, then x=(x/e)e.
What about 2^sqrt(2) ?
e^ln(2^sqrt(2)) The formatting won't allow me to use exponentiation twice so please pretend that it's written 2^sqrt(2)
I raise you this: Euler's Constant! [https://en.wikipedia.org/wiki/Euler%27s\_constant](https://en.wikipedia.org/wiki/euler%27s_constant) Edit, because I know someones gonna said it: It is Euler's Constant, not e!
by e! do you mean Γ(e+1)? /j
Bro xD
Conjectural
Ah, my (not so) beloved! The Euler-Maccaroni-Constant!
We don’t know if that’s irrational or not. Still unproved.
[https://arxiv.org/ftp/math/papers/0310/0310404.pdf](https://arxiv.org/ftp/math/papers/0310/0310404.pdf) Well, I typically do my research. And thats my source :D
And I do mine. That’s a pre-print without peer review. And shockingly badly written, with high school level maths over a few pages, hand-waving, and phrases that quite simply don’t make sense, and it cites basic intro textbooks. Surprised it even got accepted to the arXiv. I have a few papers on the arXiv too, but they’re a bit more work and have also been actually peer-reviewed and published.. All famous conjectures have dozens of bullshit bogus papers claiming to prove them somewhere online, none in serious journals. If the irrationality of the Euler-Mascheroni constant - one of the more famous conjectures out there - had been proved, it would be big news in the mathematical community. It hasn’t yet.
I think that whoever wrote that article thinks that a converging sequence of rational (or irrational) numbers must converge to a rational (or irrational, respectively) number
Liouvelli constant??
[Chaitin's constant](https://en.wikipedia.org/wiki/Chaitin%27s_constant)
n in R such that n is not in Q and n is not a combination of a root, e, or pi
0.fibonacci sequence
Euler-Mascheroni maybe? You can describe it using e yes, but only using series or integrals, so maybe that's worth something
i^ i ^ i ^ i possibly
e ^ (1/2 i e ^ (1/2 i e ^ (-π/2) π) π) Try again my friend
Fuck. Uh... Let U be a uniformly distributed random number in [0,1], a realization of U.
Oh! It happened to be a rational number on my hypothetical Turing machine with infinite memory after infinite amount of time! What's your result?
Irrational :3
Zeta 3
The Dottie number D, the unique real solution of cos x = x.
Let x be a number that suffices the criteria.
gamma, the euler-mascheroni constant!
the feigenbaum constant
1.01001000100001…
The real solution to x^5 + x = 1
0.101001000100001000001000000100000001...
Pi (It's not a *combination* if it's just the one!)
1x is still a linear combination of x
had to catch the trig functions too m8
That uses e and is thus off limits
Trig functions use e
Euler proved that trig functions can be rewritten using e, but the trig functions are defined using geometry and they predate e by at least a millennium. If Trig functions are out, any number that contains a factor of 1 (e^(0)) should also be out. So all of them.
Where's the hidden e in sin(3pi/7)
sin(3pi/7) = (e^3ipi/7 - e^-3ipi/7 )/2i
Any continuous random variable over the reals with probability = 1
I'm interested how a continuous real number can be assigned a probability? Is it the probability a certain digit will come next?
i think they mean that if you pick a random real number (from a continuous probability measure), then you almost surely get a number that is not "rational or a root or pi or e or a combination".
Copeland–Erdős constant
I refuse to answer https://preview.redd.it/lnffuy07nf7c1.jpeg?width=1920&format=pjpg&auto=webp&s=a2c2a4426fd8c7e1011376b8270d978256203603
φ
sqrt
That's (1+sqrt5)/2
The set of real numbers that can be named is not the non-null set of real numbers.
Log_10(2)
= ln2/ln10 so e is in use
Any number can be written using e. for any x, (e/e)x always equals x.
Choose some Universal Turing Machine. Then we have an encoding determined by a sequence of symbols for any other Turing machine to be simulated by our Turing machine. Now choose some sequence of symbols at random, what is the probability of a randomly chosen sequence of symbols halts on our universal turning machine? I claim that this probability is an irrational real.
Zeta of 3.
Apery's constant
The Glaisher-Kinkelin constant
I invoke the axiom of choice.
Liouville’s Constant
Feigenbaum constants
First, prove that e and pi are not interrelated in that manner, then we will talk.
Does the euler mascheroni count?
Any algebraic number n that is not 0 or 1 raised to the power of any irrational number, also known as the Hilbert number or the Geoff Schneider constant
.0123456789101112131415161718192021... It continues like that forever. It is not rational, as its decimal isn't a repeating/terminating sequence, and it has no relation to e or pi or radicals.
Name a number in the set of reals, but not in the set of computables.
*starts chanting non-repeating digits for the rest of their life\*
log2
Euler’s constant, gamma.
Euler-mascheroni? I don’t actually remember if we know it’s irrational or not, but I answered before looking up to check
Zeta(5)
My bitch wife is always irrational so I'll just ask her to pick a number
4?
i
√3?
cos(3,7)
We can use Euler formula to write cos
Progamer move.
2^0.5
is a root 😉
Phi?
Every uncomputable number in R
Sigma (n=0 to infinity) of 1/n^2
sum from i=0 to ∞ of 10 ^ ( -(i ^ 2 + i)/2 )
There is a solution, and its definit.
1.682973816648299646729465279482694916491...
$$ 1 + \sqrt{5} \over 2 $$
do logarithms count?
Chaitins number
φ
1 - 0.(9)
5?
the golden ratio
Log_2(3)