How do I define this subset using mathematical notation?Proper notation for distinct setsProof that the even natural numbers are a subset of $mathbbN$Mathematical Induction: how do we know what applies to one thing also applies to another?On the definition of cofinite.Constructing a number systemHow to correctly write this in set notation?What if there are multiple conditions in set-builder notation?Using set notation for sets with repeating charactersHow do you denote the statements $(*)$ and $(**)$ using set notation?Arbitrary Intersection between $mathbbR, N, Z$
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How do I define this subset using mathematical notation?
Proper notation for distinct setsProof that the even natural numbers are a subset of $mathbbN$Mathematical Induction: how do we know what applies to one thing also applies to another?On the definition of cofinite.Constructing a number systemHow to correctly write this in set notation?What if there are multiple conditions in set-builder notation?Using set notation for sets with repeating charactersHow do you denote the statements $(*)$ and $(**)$ using set notation?Arbitrary Intersection between $mathbbR, N, Z$
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
Assume $P = 2, 3, 5, 7, 11, 13, 17, 19, 23,....$ or in another words, P is the set consisting of all prime numbers.
Now, suppose we want to form the set $S$, which is subset of $P$,and whose elements are the first 100 prime numbers.
How do I define subset S using mathematical notation?
My two attempts were:
$S = x in P mid x ≤ m$ (where m is the 100th prime number) This method will only work when we know the exact value of is m.
$S = x_i in P mid 1 ≤ i ≤ 100$ (I believe this method is also incorrect, as sets do not support indexing)
So what will be the correct way of defining subset $S$?
elementary-set-theory
asked 10 hours ago
NelverNelver
1236 bronze badges
$endgroup$
add a comment |
$begingroup$
Assume $P = 2, 3, 5, 7, 11, 13, 17, 19, 23,....$ or in another words, P is the set consisting of all prime numbers.
Now, suppose we want to form the set $S$, which is subset of $P$,and whose elements are the first 100 prime numbers.
How do I define subset S using mathematical notation?
My two attempts were:
$S = x in P mid x ≤ m$ (where m is the 100th prime number) This method will only work when we know the exact value of is m.
$S = x_i in P mid 1 ≤ i ≤ 100$ (I believe this method is also incorrect, as sets do not support indexing)
So what will be the correct way of defining subset $S$?
elementary-set-theory
asked 10 hours ago
NelverNelver
1236 bronze badges
$endgroup$
$begingroup$
As you have started to note, i depends what mathematical notation is allowed, and you need to be clearer about what your starting point is. After all you need enough mathematical notation to define $P$ in the first place.
$endgroup$
– Mark Bennet
10 hours ago
5
$begingroup$
Also, what is the goal of this question? Often describing the set $S$ as just what it is, using natural language, is many times more clear than using convoluted mathematical expressions, just because it's possible.
$endgroup$
– Vsotvep
10 hours ago
add a comment |
$begingroup$
Assume $P = 2, 3, 5, 7, 11, 13, 17, 19, 23,....$ or in another words, P is the set consisting of all prime numbers.
Now, suppose we want to form the set $S$, which is subset of $P$,and whose elements are the first 100 prime numbers.
How do I define subset S using mathematical notation?
My two attempts were:
$S = x in P mid x ≤ m$ (where m is the 100th prime number) This method will only work when we know the exact value of is m.
$S = x_i in P mid 1 ≤ i ≤ 100$ (I believe this method is also incorrect, as sets do not support indexing)
So what will be the correct way of defining subset $S$?
elementary-set-theory
asked 10 hours ago
NelverNelver
1236 bronze badges
$endgroup$
Assume $P = 2, 3, 5, 7, 11, 13, 17, 19, 23,....$ or in another words, P is the set consisting of all prime numbers.
Now, suppose we want to form the set $S$, which is subset of $P$,and whose elements are the first 100 prime numbers.
How do I define subset S using mathematical notation?
My two attempts were:
$S = x in P mid x ≤ m$ (where m is the 100th prime number) This method will only work when we know the exact value of is m.
$S = x_i in P mid 1 ≤ i ≤ 100$ (I believe this method is also incorrect, as sets do not support indexing)
So what will be the correct way of defining subset $S$?
elementary-set-theory
elementary-set-theory
asked 10 hours ago
NelverNelver
1236 bronze badges
asked 10 hours ago
NelverNelver
1236 bronze badges
asked 10 hours ago
NelverNelver
1236 bronze badges
asked 10 hours ago
NelverNelver
1236 bronze badges
asked 10 hours ago
NelverNelver
1236 bronze badges
1236 bronze badges
$begingroup$
As you have started to note, i depends what mathematical notation is allowed, and you need to be clearer about what your starting point is. After all you need enough mathematical notation to define $P$ in the first place.
$endgroup$
– Mark Bennet
10 hours ago
5
$begingroup$
Also, what is the goal of this question? Often describing the set $S$ as just what it is, using natural language, is many times more clear than using convoluted mathematical expressions, just because it's possible.
$endgroup$
– Vsotvep
10 hours ago
add a comment |
$begingroup$
As you have started to note, i depends what mathematical notation is allowed, and you need to be clearer about what your starting point is. After all you need enough mathematical notation to define $P$ in the first place.
$endgroup$
– Mark Bennet
10 hours ago
5
$begingroup$
Also, what is the goal of this question? Often describing the set $S$ as just what it is, using natural language, is many times more clear than using convoluted mathematical expressions, just because it's possible.
$endgroup$
– Vsotvep
10 hours ago
$begingroup$
As you have started to note, i depends what mathematical notation is allowed, and you need to be clearer about what your starting point is. After all you need enough mathematical notation to define $P$ in the first place.
$endgroup$
– Mark Bennet
10 hours ago
$begingroup$
As you have started to note, i depends what mathematical notation is allowed, and you need to be clearer about what your starting point is. After all you need enough mathematical notation to define $P$ in the first place.
$endgroup$
– Mark Bennet
10 hours ago
5
5
$begingroup$
Also, what is the goal of this question? Often describing the set $S$ as just what it is, using natural language, is many times more clear than using convoluted mathematical expressions, just because it's possible.
$endgroup$
– Vsotvep
10 hours ago
$begingroup$
Also, what is the goal of this question? Often describing the set $S$ as just what it is, using natural language, is many times more clear than using convoluted mathematical expressions, just because it's possible.
$endgroup$
– Vsotvep
10 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The whole point of giving an abstract definition of the set of the first $100$ primes, is that you don't want to compute primes or use a lookup table. So in order to give the definition of the set of the first $100$ primes, it is no problem that you don't know the $100$'th prime, so I would say both approaches are fine, although I would replace $m$ in your first definition by $x_100$, or better yet, since we are talking about primes, $p_100$, where $p_i$ is the $i$'th prime.
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
$endgroup$
add a comment |
$begingroup$
It is common to use the notation $p_i$ for the $i$th prime, so you could write
$$ p_1, p_2, p_3, ldots, p_100 $$
Attempting to make it "more symbolic" (as if the mathematical notation were a programming language rather than a means of communicating ideas to human readers) will only make it less clear to your readers what you mean, and most probably will not serve any useful purpose.
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
$endgroup$
add a comment |
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2 Answers
2
active
oldest
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2 Answers
2
active
oldest
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active
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active
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$begingroup$
The whole point of giving an abstract definition of the set of the first $100$ primes, is that you don't want to compute primes or use a lookup table. So in order to give the definition of the set of the first $100$ primes, it is no problem that you don't know the $100$'th prime, so I would say both approaches are fine, although I would replace $m$ in your first definition by $x_100$, or better yet, since we are talking about primes, $p_100$, where $p_i$ is the $i$'th prime.
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
$endgroup$
add a comment |
$begingroup$
The whole point of giving an abstract definition of the set of the first $100$ primes, is that you don't want to compute primes or use a lookup table. So in order to give the definition of the set of the first $100$ primes, it is no problem that you don't know the $100$'th prime, so I would say both approaches are fine, although I would replace $m$ in your first definition by $x_100$, or better yet, since we are talking about primes, $p_100$, where $p_i$ is the $i$'th prime.
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
$endgroup$
add a comment |
$begingroup$
The whole point of giving an abstract definition of the set of the first $100$ primes, is that you don't want to compute primes or use a lookup table. So in order to give the definition of the set of the first $100$ primes, it is no problem that you don't know the $100$'th prime, so I would say both approaches are fine, although I would replace $m$ in your first definition by $x_100$, or better yet, since we are talking about primes, $p_100$, where $p_i$ is the $i$'th prime.
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
$endgroup$
The whole point of giving an abstract definition of the set of the first $100$ primes, is that you don't want to compute primes or use a lookup table. So in order to give the definition of the set of the first $100$ primes, it is no problem that you don't know the $100$'th prime, so I would say both approaches are fine, although I would replace $m$ in your first definition by $x_100$, or better yet, since we are talking about primes, $p_100$, where $p_i$ is the $i$'th prime.
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
answered 10 hours ago
Steven WagterSteven Wagter
2869 bronze badges
2869 bronze badges
add a comment |
add a comment |
$begingroup$
It is common to use the notation $p_i$ for the $i$th prime, so you could write
$$ p_1, p_2, p_3, ldots, p_100 $$
Attempting to make it "more symbolic" (as if the mathematical notation were a programming language rather than a means of communicating ideas to human readers) will only make it less clear to your readers what you mean, and most probably will not serve any useful purpose.
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
$endgroup$
add a comment |
$begingroup$
It is common to use the notation $p_i$ for the $i$th prime, so you could write
$$ p_1, p_2, p_3, ldots, p_100 $$
Attempting to make it "more symbolic" (as if the mathematical notation were a programming language rather than a means of communicating ideas to human readers) will only make it less clear to your readers what you mean, and most probably will not serve any useful purpose.
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
$endgroup$
add a comment |
$begingroup$
It is common to use the notation $p_i$ for the $i$th prime, so you could write
$$ p_1, p_2, p_3, ldots, p_100 $$
Attempting to make it "more symbolic" (as if the mathematical notation were a programming language rather than a means of communicating ideas to human readers) will only make it less clear to your readers what you mean, and most probably will not serve any useful purpose.
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
$endgroup$
It is common to use the notation $p_i$ for the $i$th prime, so you could write
$$ p_1, p_2, p_3, ldots, p_100 $$
Attempting to make it "more symbolic" (as if the mathematical notation were a programming language rather than a means of communicating ideas to human readers) will only make it less clear to your readers what you mean, and most probably will not serve any useful purpose.
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
answered 10 hours ago
Henning MakholmHenning Makholm
252k17 gold badges332 silver badges573 bronze badges
252k17 gold badges332 silver badges573 bronze badges
add a comment |
add a comment |
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$begingroup$
As you have started to note, i depends what mathematical notation is allowed, and you need to be clearer about what your starting point is. After all you need enough mathematical notation to define $P$ in the first place.
$endgroup$
– Mark Bennet
10 hours ago
5
$begingroup$
Also, what is the goal of this question? Often describing the set $S$ as just what it is, using natural language, is many times more clear than using convoluted mathematical expressions, just because it's possible.
$endgroup$
– Vsotvep
10 hours ago