What's a correct symbolism for “value that maximizes†[duplicate]
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Math notation for location of the maximum
Given a function $f(x)$, we can normally find $max_i f(i)$. This expression evaluates to the maximum value of $f(x)$. Sometimes, however, what is interesting isn't as much the maximum value itself, but the value at which the function reaches its maximum, whatever that might be:
$$i:f(i)=max_t f(t)$$
In plain English, I want to know who has eaten the most $f$ruit, rather than how much he's eaten.
This is kind of cumbersome, and perhaps needlessly requires a new symbol t. Besides, this isn't entirely correct, as $f(x)$ could very well have more than one maximum:
$$I=i:f(i)=max_tf(t)$$
Is there a nicer way to express this concept?
notation optimization
edited Apr 13 '17 at 12:20
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asked Dec 23 '11 at 0:12
badp
74611228
marked as duplicate by t.b., Srivatsan, J. M. is not a mathematician, Ilya, Asaf Karagila♦ Dec 23 '11 at 13:25
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |Â
up vote
6
down vote
favorite
Possible Duplicate:
Math notation for location of the maximum
Given a function $f(x)$, we can normally find $max_i f(i)$. This expression evaluates to the maximum value of $f(x)$. Sometimes, however, what is interesting isn't as much the maximum value itself, but the value at which the function reaches its maximum, whatever that might be:
$$i:f(i)=max_t f(t)$$
In plain English, I want to know who has eaten the most $f$ruit, rather than how much he's eaten.
This is kind of cumbersome, and perhaps needlessly requires a new symbol t. Besides, this isn't entirely correct, as $f(x)$ could very well have more than one maximum:
$$I=i:f(i)=max_tf(t)$$
Is there a nicer way to express this concept?
notation optimization
edited Apr 13 '17 at 12:20
Community♦
1
asked Dec 23 '11 at 0:12
badp
74611228
marked as duplicate by t.b., Srivatsan, J. M. is not a mathematician, Ilya, Asaf Karagila♦ Dec 23 '11 at 13:25
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
(In Italian this concept is called "punto estremante", the English Wikipedia article suggests no equivalent phrasing.)
– badp
Dec 23 '11 at 0:15
Supremum and maximum are not quite the same thing - the supremum can exist when a maximum does not.
– Thomas Andrews
Dec 23 '11 at 0:41
1
@ThomasAndrews I am very well aware. Did I make that confusion anywhere in the page?
– badp
Dec 23 '11 at 0:43
add a comment |Â
up vote
6
down vote
favorite
up vote
6
down vote
favorite
Possible Duplicate:
Math notation for location of the maximum
Given a function $f(x)$, we can normally find $max_i f(i)$. This expression evaluates to the maximum value of $f(x)$. Sometimes, however, what is interesting isn't as much the maximum value itself, but the value at which the function reaches its maximum, whatever that might be:
$$i:f(i)=max_t f(t)$$
In plain English, I want to know who has eaten the most $f$ruit, rather than how much he's eaten.
This is kind of cumbersome, and perhaps needlessly requires a new symbol t. Besides, this isn't entirely correct, as $f(x)$ could very well have more than one maximum:
$$I=i:f(i)=max_tf(t)$$
Is there a nicer way to express this concept?
notation optimization
edited Apr 13 '17 at 12:20
Community♦
1
asked Dec 23 '11 at 0:12
badp
74611228
Possible Duplicate:
Math notation for location of the maximum
Given a function $f(x)$, we can normally find $max_i f(i)$. This expression evaluates to the maximum value of $f(x)$. Sometimes, however, what is interesting isn't as much the maximum value itself, but the value at which the function reaches its maximum, whatever that might be:
$$i:f(i)=max_t f(t)$$
In plain English, I want to know who has eaten the most $f$ruit, rather than how much he's eaten.
This is kind of cumbersome, and perhaps needlessly requires a new symbol t. Besides, this isn't entirely correct, as $f(x)$ could very well have more than one maximum:
$$I=i:f(i)=max_tf(t)$$
Is there a nicer way to express this concept?
notation optimization
notation optimization
edited Apr 13 '17 at 12:20
Community♦
1
asked Dec 23 '11 at 0:12
badp
74611228
edited Apr 13 '17 at 12:20
Community♦
1
asked Dec 23 '11 at 0:12
badp
74611228
edited Apr 13 '17 at 12:20
Community♦
1
edited Apr 13 '17 at 12:20
Community♦
1
edited Apr 13 '17 at 12:20
Community♦
1
1
asked Dec 23 '11 at 0:12
badp
74611228
asked Dec 23 '11 at 0:12
badp
74611228
asked Dec 23 '11 at 0:12
badp
74611228
74611228
marked as duplicate by t.b., Srivatsan, J. M. is not a mathematician, Ilya, Asaf Karagila♦ Dec 23 '11 at 13:25
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by t.b., Srivatsan, J. M. is not a mathematician, Ilya, Asaf Karagila♦ Dec 23 '11 at 13:25
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
(In Italian this concept is called "punto estremante", the English Wikipedia article suggests no equivalent phrasing.)
– badp
Dec 23 '11 at 0:15
Supremum and maximum are not quite the same thing - the supremum can exist when a maximum does not.
– Thomas Andrews
Dec 23 '11 at 0:41
1
@ThomasAndrews I am very well aware. Did I make that confusion anywhere in the page?
– badp
Dec 23 '11 at 0:43
add a comment |Â
(In Italian this concept is called "punto estremante", the English Wikipedia article suggests no equivalent phrasing.)
– badp
Dec 23 '11 at 0:15
Supremum and maximum are not quite the same thing - the supremum can exist when a maximum does not.
– Thomas Andrews
Dec 23 '11 at 0:41
1
@ThomasAndrews I am very well aware. Did I make that confusion anywhere in the page?
– badp
Dec 23 '11 at 0:43
(In Italian this concept is called "punto estremante", the English Wikipedia article suggests no equivalent phrasing.)
– badp
Dec 23 '11 at 0:15
(In Italian this concept is called "punto estremante", the English Wikipedia article suggests no equivalent phrasing.)
– badp
Dec 23 '11 at 0:15
Supremum and maximum are not quite the same thing - the supremum can exist when a maximum does not.
– Thomas Andrews
Dec 23 '11 at 0:41
Supremum and maximum are not quite the same thing - the supremum can exist when a maximum does not.
– Thomas Andrews
Dec 23 '11 at 0:41
1
1
@ThomasAndrews I am very well aware. Did I make that confusion anywhere in the page?
– badp
Dec 23 '11 at 0:43
@ThomasAndrews I am very well aware. Did I make that confusion anywhere in the page?
– badp
Dec 23 '11 at 0:43
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
8
down vote
accepted
Often one writes $displaystyle operatorname*argmax_x f(x)$ for the value of $x$ that maximizes $f(x)$.
(Despite the fact that I have frequently seen that notation for many years, I find that it's not a standard TeX operator name; one cannot type argmax and have it understood by TeX.)
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
argmaxseems to work.
– badp
Dec 23 '11 at 0:18
1
@badp I believe your edit suggestion was made with good intentions, but I rejected it because it changed the answer too heavily. I suggest you write it as a comment instead, so that Michael can introduce that change if necessary.
– Srivatsan
Dec 23 '11 at 0:26
1
@badp : I see that you suggested argmax. Let's try that: $displaystyleargmax_x f(x)$. The subscript $x$ ends up directly below $max$ rather than symmetrically under $operatornameargmax$.
– Michael Hardy
Dec 23 '11 at 0:31
1
Wikipedia uses:underset xoperatorname arg,maxgiving: $underset xoperatorname arg,max $
– Tom Hale
Aug 4 '17 at 12:10
1
@TomHale : $uparrow$ (Just in case you missed this.)
– Michael Hardy
Aug 10 '17 at 20:53
 |Â
show 4 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
8
down vote
accepted
Often one writes $displaystyle operatorname*argmax_x f(x)$ for the value of $x$ that maximizes $f(x)$.
(Despite the fact that I have frequently seen that notation for many years, I find that it's not a standard TeX operator name; one cannot type argmax and have it understood by TeX.)
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
argmaxseems to work.
– badp
Dec 23 '11 at 0:18
1
@badp I believe your edit suggestion was made with good intentions, but I rejected it because it changed the answer too heavily. I suggest you write it as a comment instead, so that Michael can introduce that change if necessary.
– Srivatsan
Dec 23 '11 at 0:26
1
@badp : I see that you suggested argmax. Let's try that: $displaystyleargmax_x f(x)$. The subscript $x$ ends up directly below $max$ rather than symmetrically under $operatornameargmax$.
– Michael Hardy
Dec 23 '11 at 0:31
1
Wikipedia uses:underset xoperatorname arg,maxgiving: $underset xoperatorname arg,max $
– Tom Hale
Aug 4 '17 at 12:10
1
@TomHale : $uparrow$ (Just in case you missed this.)
– Michael Hardy
Aug 10 '17 at 20:53
 |Â
show 4 more comments
up vote
8
down vote
accepted
Often one writes $displaystyle operatorname*argmax_x f(x)$ for the value of $x$ that maximizes $f(x)$.
(Despite the fact that I have frequently seen that notation for many years, I find that it's not a standard TeX operator name; one cannot type argmax and have it understood by TeX.)
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
argmaxseems to work.
– badp
Dec 23 '11 at 0:18
1
@badp I believe your edit suggestion was made with good intentions, but I rejected it because it changed the answer too heavily. I suggest you write it as a comment instead, so that Michael can introduce that change if necessary.
– Srivatsan
Dec 23 '11 at 0:26
1
@badp : I see that you suggested argmax. Let's try that: $displaystyleargmax_x f(x)$. The subscript $x$ ends up directly below $max$ rather than symmetrically under $operatornameargmax$.
– Michael Hardy
Dec 23 '11 at 0:31
1
Wikipedia uses:underset xoperatorname arg,maxgiving: $underset xoperatorname arg,max $
– Tom Hale
Aug 4 '17 at 12:10
1
@TomHale : $uparrow$ (Just in case you missed this.)
– Michael Hardy
Aug 10 '17 at 20:53
 |Â
show 4 more comments
up vote
8
down vote
accepted
up vote
8
down vote
accepted
Often one writes $displaystyle operatorname*argmax_x f(x)$ for the value of $x$ that maximizes $f(x)$.
(Despite the fact that I have frequently seen that notation for many years, I find that it's not a standard TeX operator name; one cannot type argmax and have it understood by TeX.)
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
Often one writes $displaystyle operatorname*argmax_x f(x)$ for the value of $x$ that maximizes $f(x)$.
(Despite the fact that I have frequently seen that notation for many years, I find that it's not a standard TeX operator name; one cannot type argmax and have it understood by TeX.)
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
edited Aug 4 '17 at 17:46
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
answered Dec 23 '11 at 0:14
Michael Hardy
206k23187466
206k23187466
argmaxseems to work.
– badp
Dec 23 '11 at 0:18
1
@badp I believe your edit suggestion was made with good intentions, but I rejected it because it changed the answer too heavily. I suggest you write it as a comment instead, so that Michael can introduce that change if necessary.
– Srivatsan
Dec 23 '11 at 0:26
1
@badp : I see that you suggested argmax. Let's try that: $displaystyleargmax_x f(x)$. The subscript $x$ ends up directly below $max$ rather than symmetrically under $operatornameargmax$.
– Michael Hardy
Dec 23 '11 at 0:31
1
Wikipedia uses:underset xoperatorname arg,maxgiving: $underset xoperatorname arg,max $
– Tom Hale
Aug 4 '17 at 12:10
1
@TomHale : $uparrow$ (Just in case you missed this.)
– Michael Hardy
Aug 10 '17 at 20:53
 |Â
show 4 more comments
argmaxseems to work.
– badp
Dec 23 '11 at 0:18
1
@badp I believe your edit suggestion was made with good intentions, but I rejected it because it changed the answer too heavily. I suggest you write it as a comment instead, so that Michael can introduce that change if necessary.
– Srivatsan
Dec 23 '11 at 0:26
1
@badp : I see that you suggested argmax. Let's try that: $displaystyleargmax_x f(x)$. The subscript $x$ ends up directly below $max$ rather than symmetrically under $operatornameargmax$.
– Michael Hardy
Dec 23 '11 at 0:31
1
Wikipedia uses:underset xoperatorname arg,maxgiving: $underset xoperatorname arg,max $
– Tom Hale
Aug 4 '17 at 12:10
1
@TomHale : $uparrow$ (Just in case you missed this.)
– Michael Hardy
Aug 10 '17 at 20:53
argmax seems to work.– badp
Dec 23 '11 at 0:18
argmax seems to work.– badp
Dec 23 '11 at 0:18
1
1
@badp I believe your edit suggestion was made with good intentions, but I rejected it because it changed the answer too heavily. I suggest you write it as a comment instead, so that Michael can introduce that change if necessary.
– Srivatsan
Dec 23 '11 at 0:26
@badp I believe your edit suggestion was made with good intentions, but I rejected it because it changed the answer too heavily. I suggest you write it as a comment instead, so that Michael can introduce that change if necessary.
– Srivatsan
Dec 23 '11 at 0:26
1
1
@badp : I see that you suggested argmax. Let's try that: $displaystyleargmax_x f(x)$. The subscript $x$ ends up directly below $max$ rather than symmetrically under $operatornameargmax$.
– Michael Hardy
Dec 23 '11 at 0:31
@badp : I see that you suggested argmax. Let's try that: $displaystyleargmax_x f(x)$. The subscript $x$ ends up directly below $max$ rather than symmetrically under $operatornameargmax$.
– Michael Hardy
Dec 23 '11 at 0:31
1
1
Wikipedia uses:
underset xoperatorname arg,max giving: $underset xoperatorname arg,max $– Tom Hale
Aug 4 '17 at 12:10
Wikipedia uses:
underset xoperatorname arg,max giving: $underset xoperatorname arg,max $– Tom Hale
Aug 4 '17 at 12:10
1
1
@TomHale : $uparrow$ (Just in case you missed this.)
– Michael Hardy
Aug 10 '17 at 20:53
@TomHale : $uparrow$ (Just in case you missed this.)
– Michael Hardy
Aug 10 '17 at 20:53
 |Â
show 4 more comments
(In Italian this concept is called "punto estremante", the English Wikipedia article suggests no equivalent phrasing.)
– badp
Dec 23 '11 at 0:15
Supremum and maximum are not quite the same thing - the supremum can exist when a maximum does not.
– Thomas Andrews
Dec 23 '11 at 0:41
1
@ThomasAndrews I am very well aware. Did I make that confusion anywhere in the page?
– badp
Dec 23 '11 at 0:43