Mixing
Z_t is not a function [closed]
Clash Royale CLAN TAG#URR8PPP
up vote
-2
down vote
favorite
In your paper https://arxiv.org/pdf/1710.03870.pdf, at definition 4.0.3 page 12, I think there a little error.
$$Z_t(hatY_0) =
begincases
1, & A:=bigcup_k=1^nR_t^k,age 1 cap bigcup_k=1^nR_t^k,bge 1 not= emptyset,\
-1, & B:=bigcup_k=1^nR_t^k,a < 1 cap bigcup_k=1^nR_t^k,b < 1 not= emptyset,\
0, & (A bigcup B)^c not= emptyset,\
endcases$$
$Z_t$ is not well define because it is not a function. It can take more than 2 values for a unique $Ŷ_0$. $A$ and $B$ might be non-empty at the same time. Am I wrong? If not, how to fix that error?
finance
asked Aug 2 at 0:36
Jeremie
103
closed as off-topic by Will Jagy, Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy Aug 2 at 10:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy
add a comment |Â
up vote
-2
down vote
favorite
In your paper https://arxiv.org/pdf/1710.03870.pdf, at definition 4.0.3 page 12, I think there a little error.
$$Z_t(hatY_0) =
begincases
1, & A:=bigcup_k=1^nR_t^k,age 1 cap bigcup_k=1^nR_t^k,bge 1 not= emptyset,\
-1, & B:=bigcup_k=1^nR_t^k,a < 1 cap bigcup_k=1^nR_t^k,b < 1 not= emptyset,\
0, & (A bigcup B)^c not= emptyset,\
endcases$$
$Z_t$ is not well define because it is not a function. It can take more than 2 values for a unique $Ŷ_0$. $A$ and $B$ might be non-empty at the same time. Am I wrong? If not, how to fix that error?
finance
asked Aug 2 at 0:36
Jeremie
103
closed as off-topic by Will Jagy, Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy Aug 2 at 10:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy
4
It's not my paper.
– Arnaud Mortier
Aug 2 at 0:49
1
Jokes apart, you should not expect people to read a whole paper to understand what the $R$ variables are, how the RHS actually depends on $hatY_0$, whatever $hatY_0$ means, with the risk that in the end, it turns out that you misread a comma.
– Arnaud Mortier
Aug 2 at 0:53
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
In your paper https://arxiv.org/pdf/1710.03870.pdf, at definition 4.0.3 page 12, I think there a little error.
$$Z_t(hatY_0) =
begincases
1, & A:=bigcup_k=1^nR_t^k,age 1 cap bigcup_k=1^nR_t^k,bge 1 not= emptyset,\
-1, & B:=bigcup_k=1^nR_t^k,a < 1 cap bigcup_k=1^nR_t^k,b < 1 not= emptyset,\
0, & (A bigcup B)^c not= emptyset,\
endcases$$
$Z_t$ is not well define because it is not a function. It can take more than 2 values for a unique $Ŷ_0$. $A$ and $B$ might be non-empty at the same time. Am I wrong? If not, how to fix that error?
finance
asked Aug 2 at 0:36
Jeremie
103
In your paper https://arxiv.org/pdf/1710.03870.pdf, at definition 4.0.3 page 12, I think there a little error.
$$Z_t(hatY_0) =
begincases
1, & A:=bigcup_k=1^nR_t^k,age 1 cap bigcup_k=1^nR_t^k,bge 1 not= emptyset,\
-1, & B:=bigcup_k=1^nR_t^k,a < 1 cap bigcup_k=1^nR_t^k,b < 1 not= emptyset,\
0, & (A bigcup B)^c not= emptyset,\
endcases$$
$Z_t$ is not well define because it is not a function. It can take more than 2 values for a unique $Ŷ_0$. $A$ and $B$ might be non-empty at the same time. Am I wrong? If not, how to fix that error?
finance
asked Aug 2 at 0:36
Jeremie
103
edited Aug 2 at 0:59
asked Aug 2 at 0:36
Jeremie
103
asked Aug 2 at 0:36
Jeremie
103
asked Aug 2 at 0:36
Jeremie
103
103
closed as off-topic by Will Jagy, Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy Aug 2 at 10:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy
closed as off-topic by Will Jagy, Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy Aug 2 at 10:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Leucippus, Mostafa Ayaz, amWhy
4
It's not my paper.
– Arnaud Mortier
Aug 2 at 0:49
1
Jokes apart, you should not expect people to read a whole paper to understand what the $R$ variables are, how the RHS actually depends on $hatY_0$, whatever $hatY_0$ means, with the risk that in the end, it turns out that you misread a comma.
– Arnaud Mortier
Aug 2 at 0:53
add a comment |Â
4
It's not my paper.
– Arnaud Mortier
Aug 2 at 0:49
1
Jokes apart, you should not expect people to read a whole paper to understand what the $R$ variables are, how the RHS actually depends on $hatY_0$, whatever $hatY_0$ means, with the risk that in the end, it turns out that you misread a comma.
– Arnaud Mortier
Aug 2 at 0:53
4
4
It's not my paper.
– Arnaud Mortier
Aug 2 at 0:49
It's not my paper.
– Arnaud Mortier
Aug 2 at 0:49
1
1
Jokes apart, you should not expect people to read a whole paper to understand what the $R$ variables are, how the RHS actually depends on $hatY_0$, whatever $hatY_0$ means, with the risk that in the end, it turns out that you misread a comma.
– Arnaud Mortier
Aug 2 at 0:53
Jokes apart, you should not expect people to read a whole paper to understand what the $R$ variables are, how the RHS actually depends on $hatY_0$, whatever $hatY_0$ means, with the risk that in the end, it turns out that you misread a comma.
– Arnaud Mortier
Aug 2 at 0:53
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
The definition of $,A,B,$ implies that $,A cap B = emptyset,$ since, for example, $,R_t^k,age 1,$ and $,R_t^k,alt 1,$ are mutually exclusive.
Therefore the definition of $,Z_t,$ is of the following form, which is well defined because the three cases are mutually disjoint, and their union covers the applicable universe:
$$Z_t(hatY_0) =
begincases
1, & hatY_0 in A \
-1, & hatY_0 in B \
0, & hatY_0 notin A bigcup B \
endcases$$
answered Aug 2 at 0:52
dxiv
53.7k64796
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
The definition of $,A,B,$ implies that $,A cap B = emptyset,$ since, for example, $,R_t^k,age 1,$ and $,R_t^k,alt 1,$ are mutually exclusive.
Therefore the definition of $,Z_t,$ is of the following form, which is well defined because the three cases are mutually disjoint, and their union covers the applicable universe:
$$Z_t(hatY_0) =
begincases
1, & hatY_0 in A \
-1, & hatY_0 in B \
0, & hatY_0 notin A bigcup B \
endcases$$
answered Aug 2 at 0:52
dxiv
53.7k64796
add a comment |Â
up vote
3
down vote
accepted
The definition of $,A,B,$ implies that $,A cap B = emptyset,$ since, for example, $,R_t^k,age 1,$ and $,R_t^k,alt 1,$ are mutually exclusive.
Therefore the definition of $,Z_t,$ is of the following form, which is well defined because the three cases are mutually disjoint, and their union covers the applicable universe:
$$Z_t(hatY_0) =
begincases
1, & hatY_0 in A \
-1, & hatY_0 in B \
0, & hatY_0 notin A bigcup B \
endcases$$
answered Aug 2 at 0:52
dxiv
53.7k64796
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
The definition of $,A,B,$ implies that $,A cap B = emptyset,$ since, for example, $,R_t^k,age 1,$ and $,R_t^k,alt 1,$ are mutually exclusive.
Therefore the definition of $,Z_t,$ is of the following form, which is well defined because the three cases are mutually disjoint, and their union covers the applicable universe:
$$Z_t(hatY_0) =
begincases
1, & hatY_0 in A \
-1, & hatY_0 in B \
0, & hatY_0 notin A bigcup B \
endcases$$
answered Aug 2 at 0:52
dxiv
53.7k64796
The definition of $,A,B,$ implies that $,A cap B = emptyset,$ since, for example, $,R_t^k,age 1,$ and $,R_t^k,alt 1,$ are mutually exclusive.
Therefore the definition of $,Z_t,$ is of the following form, which is well defined because the three cases are mutually disjoint, and their union covers the applicable universe:
$$Z_t(hatY_0) =
begincases
1, & hatY_0 in A \
-1, & hatY_0 in B \
0, & hatY_0 notin A bigcup B \
endcases$$
answered Aug 2 at 0:52
dxiv
53.7k64796
edited Aug 2 at 1:06
answered Aug 2 at 0:52
dxiv
53.7k64796
answered Aug 2 at 0:52
dxiv
53.7k64796
answered Aug 2 at 0:52
dxiv
53.7k64796
53.7k64796
add a comment |Â
add a comment |Â
4
It's not my paper.
– Arnaud Mortier
Aug 2 at 0:49
1
Jokes apart, you should not expect people to read a whole paper to understand what the $R$ variables are, how the RHS actually depends on $hatY_0$, whatever $hatY_0$ means, with the risk that in the end, it turns out that you misread a comma.
– Arnaud Mortier
Aug 2 at 0:53