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What does this $asymp$ symbol mean? (subject: analytic number theory)
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I'm reading a survey article by Andrew Granville on analytic number theory.
On page 22 of the paper, there appears a strange looking symbol, undefined. I've circled it in red in the screenshot below.
Since it's not defined in the paper, I'm assuming it must be standard notation.
From the context, I'm assuming it means something like "as compared to", or "with reference to", but that's just a guess.
Can anyone identify the symbol, even better explain what it means and/or provide a reference? Is there a name to speak the symbol?
Thanks in advance.
analysis notation asymptotics analytic-number-theory
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
add a comment |
up vote
7
down vote
favorite
I'm reading a survey article by Andrew Granville on analytic number theory.
On page 22 of the paper, there appears a strange looking symbol, undefined. I've circled it in red in the screenshot below.
Since it's not defined in the paper, I'm assuming it must be standard notation.
From the context, I'm assuming it means something like "as compared to", or "with reference to", but that's just a guess.
Can anyone identify the symbol, even better explain what it means and/or provide a reference? Is there a name to speak the symbol?
Thanks in advance.
analysis notation asymptotics analytic-number-theory
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
add a comment |
up vote
7
down vote
favorite
up vote
7
down vote
favorite
I'm reading a survey article by Andrew Granville on analytic number theory.
On page 22 of the paper, there appears a strange looking symbol, undefined. I've circled it in red in the screenshot below.
Since it's not defined in the paper, I'm assuming it must be standard notation.
From the context, I'm assuming it means something like "as compared to", or "with reference to", but that's just a guess.
Can anyone identify the symbol, even better explain what it means and/or provide a reference? Is there a name to speak the symbol?
Thanks in advance.
analysis notation asymptotics analytic-number-theory
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
I'm reading a survey article by Andrew Granville on analytic number theory.
On page 22 of the paper, there appears a strange looking symbol, undefined. I've circled it in red in the screenshot below.
Since it's not defined in the paper, I'm assuming it must be standard notation.
From the context, I'm assuming it means something like "as compared to", or "with reference to", but that's just a guess.
Can anyone identify the symbol, even better explain what it means and/or provide a reference? Is there a name to speak the symbol?
Thanks in advance.
analysis notation asymptotics analytic-number-theory
analysis notation asymptotics analytic-number-theory
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
edited Apr 23 '14 at 11:41
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
asked Apr 22 '14 at 19:24
Assad Ebrahim
621621
621621
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
up vote
5
down vote
accepted
It can mean different things depending on the context. For instance, in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big $Theta$" (see p. 448), as in
$$
f asymp g iff exists, C,D>0 : C|g| leq |f| leq D|g|,
$$
but I read a paper recently where it was instead defined to mean the same thing as $sim$ (as defined here).
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
Yes, I think you're right. Having looked at your LaTeX code, I see the symbol isasymp, and doing a search brings up this useful table on asymptotic notations that confirms your (nicer) expression above. (I'll paste the table into a separate answer below for reference.) Accepting your answer as the correct one. Thanks!
– Assad Ebrahim
Apr 22 '14 at 20:44
1
(+1)... in English: "there exist positive constants C,D such that $f$ can be sandwiched between $g$ scaled appropriately above and below."
– Assad Ebrahim
Apr 22 '14 at 20:56
add a comment |
up vote
4
down vote
Searching further on Antonio Vargas's accepted answer above finds an insightful short paper of A.J. Hildebrand on Asymptotic Notation.
From this the following useful reference table is screenshotted below:
edited yesterday
malin
718620
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
It can mean different things depending on the context. For instance, in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big $Theta$" (see p. 448), as in
$$
f asymp g iff exists, C,D>0 : C|g| leq |f| leq D|g|,
$$
but I read a paper recently where it was instead defined to mean the same thing as $sim$ (as defined here).
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
Yes, I think you're right. Having looked at your LaTeX code, I see the symbol isasymp, and doing a search brings up this useful table on asymptotic notations that confirms your (nicer) expression above. (I'll paste the table into a separate answer below for reference.) Accepting your answer as the correct one. Thanks!
– Assad Ebrahim
Apr 22 '14 at 20:44
1
(+1)... in English: "there exist positive constants C,D such that $f$ can be sandwiched between $g$ scaled appropriately above and below."
– Assad Ebrahim
Apr 22 '14 at 20:56
add a comment |
up vote
5
down vote
accepted
It can mean different things depending on the context. For instance, in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big $Theta$" (see p. 448), as in
$$
f asymp g iff exists, C,D>0 : C|g| leq |f| leq D|g|,
$$
but I read a paper recently where it was instead defined to mean the same thing as $sim$ (as defined here).
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
Yes, I think you're right. Having looked at your LaTeX code, I see the symbol isasymp, and doing a search brings up this useful table on asymptotic notations that confirms your (nicer) expression above. (I'll paste the table into a separate answer below for reference.) Accepting your answer as the correct one. Thanks!
– Assad Ebrahim
Apr 22 '14 at 20:44
1
(+1)... in English: "there exist positive constants C,D such that $f$ can be sandwiched between $g$ scaled appropriately above and below."
– Assad Ebrahim
Apr 22 '14 at 20:56
add a comment |
up vote
5
down vote
accepted
up vote
5
down vote
accepted
It can mean different things depending on the context. For instance, in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big $Theta$" (see p. 448), as in
$$
f asymp g iff exists, C,D>0 : C|g| leq |f| leq D|g|,
$$
but I read a paper recently where it was instead defined to mean the same thing as $sim$ (as defined here).
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
It can mean different things depending on the context. For instance, in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big $Theta$" (see p. 448), as in
$$
f asymp g iff exists, C,D>0 : C|g| leq |f| leq D|g|,
$$
but I read a paper recently where it was instead defined to mean the same thing as $sim$ (as defined here).
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
answered Apr 22 '14 at 19:54
Antonio Vargas
20.6k244111
20.6k244111
Yes, I think you're right. Having looked at your LaTeX code, I see the symbol isasymp, and doing a search brings up this useful table on asymptotic notations that confirms your (nicer) expression above. (I'll paste the table into a separate answer below for reference.) Accepting your answer as the correct one. Thanks!
– Assad Ebrahim
Apr 22 '14 at 20:44
1
(+1)... in English: "there exist positive constants C,D such that $f$ can be sandwiched between $g$ scaled appropriately above and below."
– Assad Ebrahim
Apr 22 '14 at 20:56
add a comment |
Yes, I think you're right. Having looked at your LaTeX code, I see the symbol isasymp, and doing a search brings up this useful table on asymptotic notations that confirms your (nicer) expression above. (I'll paste the table into a separate answer below for reference.) Accepting your answer as the correct one. Thanks!
– Assad Ebrahim
Apr 22 '14 at 20:44
1
(+1)... in English: "there exist positive constants C,D such that $f$ can be sandwiched between $g$ scaled appropriately above and below."
– Assad Ebrahim
Apr 22 '14 at 20:56
Yes, I think you're right. Having looked at your LaTeX code, I see the symbol is
asymp, and doing a search brings up this useful table on asymptotic notations that confirms your (nicer) expression above. (I'll paste the table into a separate answer below for reference.) Accepting your answer as the correct one. Thanks!– Assad Ebrahim
Apr 22 '14 at 20:44
Yes, I think you're right. Having looked at your LaTeX code, I see the symbol is
asymp, and doing a search brings up this useful table on asymptotic notations that confirms your (nicer) expression above. (I'll paste the table into a separate answer below for reference.) Accepting your answer as the correct one. Thanks!– Assad Ebrahim
Apr 22 '14 at 20:44
1
1
(+1)... in English: "there exist positive constants C,D such that $f$ can be sandwiched between $g$ scaled appropriately above and below."
– Assad Ebrahim
Apr 22 '14 at 20:56
(+1)... in English: "there exist positive constants C,D such that $f$ can be sandwiched between $g$ scaled appropriately above and below."
– Assad Ebrahim
Apr 22 '14 at 20:56
add a comment |
up vote
4
down vote
Searching further on Antonio Vargas's accepted answer above finds an insightful short paper of A.J. Hildebrand on Asymptotic Notation.
From this the following useful reference table is screenshotted below:
edited yesterday
malin
718620
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
add a comment |
up vote
4
down vote
Searching further on Antonio Vargas's accepted answer above finds an insightful short paper of A.J. Hildebrand on Asymptotic Notation.
From this the following useful reference table is screenshotted below:
edited yesterday
malin
718620
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
add a comment |
up vote
4
down vote
up vote
4
down vote
Searching further on Antonio Vargas's accepted answer above finds an insightful short paper of A.J. Hildebrand on Asymptotic Notation.
From this the following useful reference table is screenshotted below:
edited yesterday
malin
718620
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
Searching further on Antonio Vargas's accepted answer above finds an insightful short paper of A.J. Hildebrand on Asymptotic Notation.
From this the following useful reference table is screenshotted below:
edited yesterday
malin
718620
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
edited yesterday
malin
718620
edited yesterday
malin
718620
edited yesterday
malin
718620
718620
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
answered Apr 22 '14 at 20:51
Assad Ebrahim
621621
621621
add a comment |
add a comment |
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