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Is there any function whose limit at $x_0$ is uknown?
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I would like to know if there is any non trivial function $f(x)$ and a $x_0$ such that $$lim_xto x_0 f(x)$$
is currently not known, with $x_0 in mathbbRcup -infty, +infty $.
An example of a "trivial" function is $A(x)$ where $A(x)$ denotes the number of perfect numbers not greater than $x$. It is an open problem to find the value of $lim_xtoinfty A(x)$, since we don't know if there are infinitely many perfect numbers.
I would prefer a limit which can be recognized by a high school student.
real-analysis limits open-problem
asked Jul 24 at 7:32
Konstantinos Gaitanas
6,54131838
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up vote
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I would like to know if there is any non trivial function $f(x)$ and a $x_0$ such that $$lim_xto x_0 f(x)$$
is currently not known, with $x_0 in mathbbRcup -infty, +infty $.
An example of a "trivial" function is $A(x)$ where $A(x)$ denotes the number of perfect numbers not greater than $x$. It is an open problem to find the value of $lim_xtoinfty A(x)$, since we don't know if there are infinitely many perfect numbers.
I would prefer a limit which can be recognized by a high school student.
real-analysis limits open-problem
asked Jul 24 at 7:32
Konstantinos Gaitanas
6,54131838
2
A slightly different example would be a function counting the integers $<x$ for which the sequence in the Collatz conjecture doesn't end at $1$ (I call it slight different because wee don't know if any such integer exist, i.e. whether the function ever becomes $neq 0$, where we know 50 perfect numbers). But that is probably also trivial, but you haven't given us a definition of trivial that is actually workable.
– Henrik
Jul 24 at 8:08
1
The value of $$lim_ntoinftyR(n,n)^frac1n$$ where $R(n,n)$ is a so-called Ramsey number is unknown. It is known that the limit (if it exists) lies in the interval $[sqrt2,4].$
– bof
Jul 24 at 8:42
add a comment |Â
up vote
5
down vote
favorite
up vote
5
down vote
favorite
I would like to know if there is any non trivial function $f(x)$ and a $x_0$ such that $$lim_xto x_0 f(x)$$
is currently not known, with $x_0 in mathbbRcup -infty, +infty $.
An example of a "trivial" function is $A(x)$ where $A(x)$ denotes the number of perfect numbers not greater than $x$. It is an open problem to find the value of $lim_xtoinfty A(x)$, since we don't know if there are infinitely many perfect numbers.
I would prefer a limit which can be recognized by a high school student.
real-analysis limits open-problem
asked Jul 24 at 7:32
Konstantinos Gaitanas
6,54131838
I would like to know if there is any non trivial function $f(x)$ and a $x_0$ such that $$lim_xto x_0 f(x)$$
is currently not known, with $x_0 in mathbbRcup -infty, +infty $.
An example of a "trivial" function is $A(x)$ where $A(x)$ denotes the number of perfect numbers not greater than $x$. It is an open problem to find the value of $lim_xtoinfty A(x)$, since we don't know if there are infinitely many perfect numbers.
I would prefer a limit which can be recognized by a high school student.
real-analysis limits open-problem
asked Jul 24 at 7:32
Konstantinos Gaitanas
6,54131838
asked Jul 24 at 7:32
Konstantinos Gaitanas
6,54131838
asked Jul 24 at 7:32
Konstantinos Gaitanas
6,54131838
asked Jul 24 at 7:32
Konstantinos Gaitanas
6,54131838
6,54131838
2
A slightly different example would be a function counting the integers $<x$ for which the sequence in the Collatz conjecture doesn't end at $1$ (I call it slight different because wee don't know if any such integer exist, i.e. whether the function ever becomes $neq 0$, where we know 50 perfect numbers). But that is probably also trivial, but you haven't given us a definition of trivial that is actually workable.
– Henrik
Jul 24 at 8:08
1
The value of $$lim_ntoinftyR(n,n)^frac1n$$ where $R(n,n)$ is a so-called Ramsey number is unknown. It is known that the limit (if it exists) lies in the interval $[sqrt2,4].$
– bof
Jul 24 at 8:42
add a comment |Â
2
A slightly different example would be a function counting the integers $<x$ for which the sequence in the Collatz conjecture doesn't end at $1$ (I call it slight different because wee don't know if any such integer exist, i.e. whether the function ever becomes $neq 0$, where we know 50 perfect numbers). But that is probably also trivial, but you haven't given us a definition of trivial that is actually workable.
– Henrik
Jul 24 at 8:08
1
The value of $$lim_ntoinftyR(n,n)^frac1n$$ where $R(n,n)$ is a so-called Ramsey number is unknown. It is known that the limit (if it exists) lies in the interval $[sqrt2,4].$
– bof
Jul 24 at 8:42
2
2
A slightly different example would be a function counting the integers $<x$ for which the sequence in the Collatz conjecture doesn't end at $1$ (I call it slight different because wee don't know if any such integer exist, i.e. whether the function ever becomes $neq 0$, where we know 50 perfect numbers). But that is probably also trivial, but you haven't given us a definition of trivial that is actually workable.
– Henrik
Jul 24 at 8:08
A slightly different example would be a function counting the integers $<x$ for which the sequence in the Collatz conjecture doesn't end at $1$ (I call it slight different because wee don't know if any such integer exist, i.e. whether the function ever becomes $neq 0$, where we know 50 perfect numbers). But that is probably also trivial, but you haven't given us a definition of trivial that is actually workable.
– Henrik
Jul 24 at 8:08
1
1
The value of $$lim_ntoinftyR(n,n)^frac1n$$ where $R(n,n)$ is a so-called Ramsey number is unknown. It is known that the limit (if it exists) lies in the interval $[sqrt2,4].$
– bof
Jul 24 at 8:42
The value of $$lim_ntoinftyR(n,n)^frac1n$$ where $R(n,n)$ is a so-called Ramsey number is unknown. It is known that the limit (if it exists) lies in the interval $[sqrt2,4].$
– bof
Jul 24 at 8:42
add a comment |Â
1 Answer
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Brun's theorem states that the sum of reciprocals of twin primes is convergent, but there is no other known expression for the limit.
answered Jul 24 at 8:40
Ludvig Lindström
585
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Brun's theorem states that the sum of reciprocals of twin primes is convergent, but there is no other known expression for the limit.
answered Jul 24 at 8:40
Ludvig Lindström
585
add a comment |Â
up vote
1
down vote
Brun's theorem states that the sum of reciprocals of twin primes is convergent, but there is no other known expression for the limit.
answered Jul 24 at 8:40
Ludvig Lindström
585
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Brun's theorem states that the sum of reciprocals of twin primes is convergent, but there is no other known expression for the limit.
answered Jul 24 at 8:40
Ludvig Lindström
585
Brun's theorem states that the sum of reciprocals of twin primes is convergent, but there is no other known expression for the limit.
answered Jul 24 at 8:40
Ludvig Lindström
585
answered Jul 24 at 8:40
Ludvig Lindström
585
answered Jul 24 at 8:40
Ludvig Lindström
585
answered Jul 24 at 8:40
Ludvig Lindström
585
585
add a comment |Â
add a comment |Â
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2
A slightly different example would be a function counting the integers $<x$ for which the sequence in the Collatz conjecture doesn't end at $1$ (I call it slight different because wee don't know if any such integer exist, i.e. whether the function ever becomes $neq 0$, where we know 50 perfect numbers). But that is probably also trivial, but you haven't given us a definition of trivial that is actually workable.
– Henrik
Jul 24 at 8:08
1
The value of $$lim_ntoinftyR(n,n)^frac1n$$ where $R(n,n)$ is a so-called Ramsey number is unknown. It is known that the limit (if it exists) lies in the interval $[sqrt2,4].$
– bof
Jul 24 at 8:42