Mixing
Regular set definition
Clash Royale CLAN TAG#URR8PPP
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I came across the following regular sets definition:
Let Σ be a finite alphabet. Regular sets over Σ are defined recursively as
follows:
- ∅ (i. e. an empty set) is a regular set over Σ,
- ε is a regular set over Σ,
- a is a regular set over Σ for all a ∈ Σ,
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q,
(c) P ∗
are the regular sets over Σ.
- Nothing else is a regular set.
I cannot understand why is this definition complete. What I gather from points 4. and 5. is that
Q.P and Q * are not a regular set. Why doesn't 4. look like this?
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q, Q.P
(c) P ∗, Q *
are the regular sets over Σ.
regular-expressions
asked yesterday
Milda
1
 |Â
show 2 more comments
up vote
0
down vote
favorite
I came across the following regular sets definition:
Let Σ be a finite alphabet. Regular sets over Σ are defined recursively as
follows:
- ∅ (i. e. an empty set) is a regular set over Σ,
- ε is a regular set over Σ,
- a is a regular set over Σ for all a ∈ Σ,
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q,
(c) P ∗
are the regular sets over Σ.
- Nothing else is a regular set.
I cannot understand why is this definition complete. What I gather from points 4. and 5. is that
Q.P and Q * are not a regular set. Why doesn't 4. look like this?
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q, Q.P
(c) P ∗, Q *
are the regular sets over Σ.
regular-expressions
asked yesterday
Milda
1
That would be redundant.
– Lord Shark the Unknown
yesterday
I must be missing something. If P = abc and Q = def, how can I get Q.P defabc using P.Q and nothing else?
– Milda
yesterday
How about taking $Q=abc$, $P=def$?
– Lord Shark the Unknown
yesterday
Ah, I see. Sorry if this seems dumb, my math is mostly self-thought. Is there a way to define the rules the way I interpreted it? Where Q.P and Q * would be excluded?
– Milda
yesterday
Why do you want to exclude $P.Q$ and $P^*$?
– Lord Shark the Unknown
yesterday
 |Â
show 2 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I came across the following regular sets definition:
Let Σ be a finite alphabet. Regular sets over Σ are defined recursively as
follows:
- ∅ (i. e. an empty set) is a regular set over Σ,
- ε is a regular set over Σ,
- a is a regular set over Σ for all a ∈ Σ,
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q,
(c) P ∗
are the regular sets over Σ.
- Nothing else is a regular set.
I cannot understand why is this definition complete. What I gather from points 4. and 5. is that
Q.P and Q * are not a regular set. Why doesn't 4. look like this?
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q, Q.P
(c) P ∗, Q *
are the regular sets over Σ.
regular-expressions
asked yesterday
Milda
1
I came across the following regular sets definition:
Let Σ be a finite alphabet. Regular sets over Σ are defined recursively as
follows:
- ∅ (i. e. an empty set) is a regular set over Σ,
- ε is a regular set over Σ,
- a is a regular set over Σ for all a ∈ Σ,
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q,
(c) P ∗
are the regular sets over Σ.
- Nothing else is a regular set.
I cannot understand why is this definition complete. What I gather from points 4. and 5. is that
Q.P and Q * are not a regular set. Why doesn't 4. look like this?
- if P and Q are the regular sets over Σ, then also
(a) P ∪ Q,
(b) P.Q, Q.P
(c) P ∗, Q *
are the regular sets over Σ.
regular-expressions
asked yesterday
Milda
1
asked yesterday
Milda
1
asked yesterday
Milda
1
asked yesterday
Milda
1
1
That would be redundant.
– Lord Shark the Unknown
yesterday
I must be missing something. If P = abc and Q = def, how can I get Q.P defabc using P.Q and nothing else?
– Milda
yesterday
How about taking $Q=abc$, $P=def$?
– Lord Shark the Unknown
yesterday
Ah, I see. Sorry if this seems dumb, my math is mostly self-thought. Is there a way to define the rules the way I interpreted it? Where Q.P and Q * would be excluded?
– Milda
yesterday
Why do you want to exclude $P.Q$ and $P^*$?
– Lord Shark the Unknown
yesterday
 |Â
show 2 more comments
That would be redundant.
– Lord Shark the Unknown
yesterday
I must be missing something. If P = abc and Q = def, how can I get Q.P defabc using P.Q and nothing else?
– Milda
yesterday
How about taking $Q=abc$, $P=def$?
– Lord Shark the Unknown
yesterday
Ah, I see. Sorry if this seems dumb, my math is mostly self-thought. Is there a way to define the rules the way I interpreted it? Where Q.P and Q * would be excluded?
– Milda
yesterday
Why do you want to exclude $P.Q$ and $P^*$?
– Lord Shark the Unknown
yesterday
That would be redundant.
– Lord Shark the Unknown
yesterday
That would be redundant.
– Lord Shark the Unknown
yesterday
I must be missing something. If P = abc and Q = def, how can I get Q.P defabc using P.Q and nothing else?
– Milda
yesterday
I must be missing something. If P = abc and Q = def, how can I get Q.P defabc using P.Q and nothing else?
– Milda
yesterday
How about taking $Q=abc$, $P=def$?
– Lord Shark the Unknown
yesterday
How about taking $Q=abc$, $P=def$?
– Lord Shark the Unknown
yesterday
Ah, I see. Sorry if this seems dumb, my math is mostly self-thought. Is there a way to define the rules the way I interpreted it? Where Q.P and Q * would be excluded?
– Milda
yesterday
Ah, I see. Sorry if this seems dumb, my math is mostly self-thought. Is there a way to define the rules the way I interpreted it? Where Q.P and Q * would be excluded?
– Milda
yesterday
Why do you want to exclude $P.Q$ and $P^*$?
– Lord Shark the Unknown
yesterday
Why do you want to exclude $P.Q$ and $P^*$?
– Lord Shark the Unknown
yesterday
 |Â
show 2 more comments
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That would be redundant.
– Lord Shark the Unknown
yesterday
I must be missing something. If P = abc and Q = def, how can I get Q.P defabc using P.Q and nothing else?
– Milda
yesterday
How about taking $Q=abc$, $P=def$?
– Lord Shark the Unknown
yesterday
Ah, I see. Sorry if this seems dumb, my math is mostly self-thought. Is there a way to define the rules the way I interpreted it? Where Q.P and Q * would be excluded?
– Milda
yesterday
Why do you want to exclude $P.Q$ and $P^*$?
– Lord Shark the Unknown
yesterday