Irrationality of $pi$ isn't confirmed?
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I've heard that there is a bit of argument over whether you can confirm that $pi$ is truly irrational. We know $pi$ up to 2.7 trillion digits, but that accuracy isn't even that big, especially when you compare it to how accurately we know $e$. So, is there a possibility that the digits of $pi$ will repeat or end?
number-theory
asked Dec 5 at 23:27
Xavier Stanton
330211
add a comment |
up vote
-2
down vote
favorite
I've heard that there is a bit of argument over whether you can confirm that $pi$ is truly irrational. We know $pi$ up to 2.7 trillion digits, but that accuracy isn't even that big, especially when you compare it to how accurately we know $e$. So, is there a possibility that the digits of $pi$ will repeat or end?
number-theory
asked Dec 5 at 23:27
Xavier Stanton
330211
5
$pi$ is known to be irrational.
– platty
Dec 5 at 23:28
I don't understand the downvotes. The premise of the question is wrong, but that goes straight to the purpose of the question. The OP doesn't know!
– Matt Samuel
Dec 6 at 1:21
2
@MattSamuel I guess it's related to the fact that a brief search on the internet would be sufficient for the OP to find out by himself.
– rafa11111
Dec 6 at 11:50
1
@rafa I bet the same search will also get you some wrong info.
– Matt Samuel
Dec 6 at 12:13
By the way, $pi$ has been calculated far more accurate than $e$. Irrationality proofs are extremely difficult in general, for example it is unknown whether the Euler-Mascheroni-constant is rational.
– Peter
Dec 6 at 14:12
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
I've heard that there is a bit of argument over whether you can confirm that $pi$ is truly irrational. We know $pi$ up to 2.7 trillion digits, but that accuracy isn't even that big, especially when you compare it to how accurately we know $e$. So, is there a possibility that the digits of $pi$ will repeat or end?
number-theory
asked Dec 5 at 23:27
Xavier Stanton
330211
I've heard that there is a bit of argument over whether you can confirm that $pi$ is truly irrational. We know $pi$ up to 2.7 trillion digits, but that accuracy isn't even that big, especially when you compare it to how accurately we know $e$. So, is there a possibility that the digits of $pi$ will repeat or end?
number-theory
number-theory
asked Dec 5 at 23:27
Xavier Stanton
330211
asked Dec 5 at 23:27
Xavier Stanton
330211
asked Dec 5 at 23:27
Xavier Stanton
330211
asked Dec 5 at 23:27
Xavier Stanton
330211
asked Dec 5 at 23:27
Xavier Stanton
330211
330211
5
$pi$ is known to be irrational.
– platty
Dec 5 at 23:28
I don't understand the downvotes. The premise of the question is wrong, but that goes straight to the purpose of the question. The OP doesn't know!
– Matt Samuel
Dec 6 at 1:21
2
@MattSamuel I guess it's related to the fact that a brief search on the internet would be sufficient for the OP to find out by himself.
– rafa11111
Dec 6 at 11:50
1
@rafa I bet the same search will also get you some wrong info.
– Matt Samuel
Dec 6 at 12:13
By the way, $pi$ has been calculated far more accurate than $e$. Irrationality proofs are extremely difficult in general, for example it is unknown whether the Euler-Mascheroni-constant is rational.
– Peter
Dec 6 at 14:12
add a comment |
5
$pi$ is known to be irrational.
– platty
Dec 5 at 23:28
I don't understand the downvotes. The premise of the question is wrong, but that goes straight to the purpose of the question. The OP doesn't know!
– Matt Samuel
Dec 6 at 1:21
2
@MattSamuel I guess it's related to the fact that a brief search on the internet would be sufficient for the OP to find out by himself.
– rafa11111
Dec 6 at 11:50
1
@rafa I bet the same search will also get you some wrong info.
– Matt Samuel
Dec 6 at 12:13
By the way, $pi$ has been calculated far more accurate than $e$. Irrationality proofs are extremely difficult in general, for example it is unknown whether the Euler-Mascheroni-constant is rational.
– Peter
Dec 6 at 14:12
5
5
$pi$ is known to be irrational.
– platty
Dec 5 at 23:28
$pi$ is known to be irrational.
– platty
Dec 5 at 23:28
I don't understand the downvotes. The premise of the question is wrong, but that goes straight to the purpose of the question. The OP doesn't know!
– Matt Samuel
Dec 6 at 1:21
I don't understand the downvotes. The premise of the question is wrong, but that goes straight to the purpose of the question. The OP doesn't know!
– Matt Samuel
Dec 6 at 1:21
2
2
@MattSamuel I guess it's related to the fact that a brief search on the internet would be sufficient for the OP to find out by himself.
– rafa11111
Dec 6 at 11:50
@MattSamuel I guess it's related to the fact that a brief search on the internet would be sufficient for the OP to find out by himself.
– rafa11111
Dec 6 at 11:50
1
1
@rafa I bet the same search will also get you some wrong info.
– Matt Samuel
Dec 6 at 12:13
@rafa I bet the same search will also get you some wrong info.
– Matt Samuel
Dec 6 at 12:13
By the way, $pi$ has been calculated far more accurate than $e$. Irrationality proofs are extremely difficult in general, for example it is unknown whether the Euler-Mascheroni-constant is rational.
– Peter
Dec 6 at 14:12
By the way, $pi$ has been calculated far more accurate than $e$. Irrationality proofs are extremely difficult in general, for example it is unknown whether the Euler-Mascheroni-constant is rational.
– Peter
Dec 6 at 14:12
add a comment |
1 Answer
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You can't prove irrationality by calculating digits and looking for a repeat because the repeat could start a little further out. $pi$ and $e$ are known to be transcendental, not just irrational. You may have heard that we don't know if $pi$ is normal, meaning any sequence of digits occurs with the correct limiting probability. That is correct, but most people who understand it would guess that it is.
answered Dec 5 at 23:33
Ross Millikan
290k23196369
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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oldest
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up vote
10
down vote
You can't prove irrationality by calculating digits and looking for a repeat because the repeat could start a little further out. $pi$ and $e$ are known to be transcendental, not just irrational. You may have heard that we don't know if $pi$ is normal, meaning any sequence of digits occurs with the correct limiting probability. That is correct, but most people who understand it would guess that it is.
answered Dec 5 at 23:33
Ross Millikan
290k23196369
add a comment |
up vote
10
down vote
You can't prove irrationality by calculating digits and looking for a repeat because the repeat could start a little further out. $pi$ and $e$ are known to be transcendental, not just irrational. You may have heard that we don't know if $pi$ is normal, meaning any sequence of digits occurs with the correct limiting probability. That is correct, but most people who understand it would guess that it is.
answered Dec 5 at 23:33
Ross Millikan
290k23196369
add a comment |
up vote
10
down vote
up vote
10
down vote
You can't prove irrationality by calculating digits and looking for a repeat because the repeat could start a little further out. $pi$ and $e$ are known to be transcendental, not just irrational. You may have heard that we don't know if $pi$ is normal, meaning any sequence of digits occurs with the correct limiting probability. That is correct, but most people who understand it would guess that it is.
answered Dec 5 at 23:33
Ross Millikan
290k23196369
You can't prove irrationality by calculating digits and looking for a repeat because the repeat could start a little further out. $pi$ and $e$ are known to be transcendental, not just irrational. You may have heard that we don't know if $pi$ is normal, meaning any sequence of digits occurs with the correct limiting probability. That is correct, but most people who understand it would guess that it is.
answered Dec 5 at 23:33
Ross Millikan
290k23196369
answered Dec 5 at 23:33
Ross Millikan
290k23196369
answered Dec 5 at 23:33
Ross Millikan
290k23196369
answered Dec 5 at 23:33
Ross Millikan
290k23196369
290k23196369
add a comment |
add a comment |
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5
$pi$ is known to be irrational.
– platty
Dec 5 at 23:28
I don't understand the downvotes. The premise of the question is wrong, but that goes straight to the purpose of the question. The OP doesn't know!
– Matt Samuel
Dec 6 at 1:21
2
@MattSamuel I guess it's related to the fact that a brief search on the internet would be sufficient for the OP to find out by himself.
– rafa11111
Dec 6 at 11:50
1
@rafa I bet the same search will also get you some wrong info.
– Matt Samuel
Dec 6 at 12:13
By the way, $pi$ has been calculated far more accurate than $e$. Irrationality proofs are extremely difficult in general, for example it is unknown whether the Euler-Mascheroni-constant is rational.
– Peter
Dec 6 at 14:12