How is this property called for mod?
$begingroup$
We have a name for the property of integers to be $0$ or $1$ $mathrm{mod} 2$ - parity.
Is there any similar name for the remainder for any other base? Like a generalization of parity? Could I use parity in a broader sense, just to name the remainder $mathrm{mod} n$?
elementary-number-theory soft-question integers
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
$endgroup$
add a comment |
$begingroup$
We have a name for the property of integers to be $0$ or $1$ $mathrm{mod} 2$ - parity.
Is there any similar name for the remainder for any other base? Like a generalization of parity? Could I use parity in a broader sense, just to name the remainder $mathrm{mod} n$?
elementary-number-theory soft-question integers
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
$endgroup$
9
$begingroup$
How about congruence?
$endgroup$
– Umberto P.
Feb 25 at 11:37
$begingroup$
So should I say (variable)'s congruence class or value?
$endgroup$
– dEmigOd
Feb 25 at 11:43
$begingroup$
I had the same question and thought about terminology for $n = 3$. A friend of mine came up with a very neat suggestion: flat, short and long. I don't know if there is any other generalization, but I would very much like to hear people talking about remainders mod 3 like this. I guess the reason why this has a name for $n=2$ is that it appears commonly in everyday life as opposed to most of the other numbers. When talking about time, the 12 is dropped at all, but this is somewhat different maybe
$endgroup$
– kesa
Feb 25 at 15:44
add a comment |
$begingroup$
We have a name for the property of integers to be $0$ or $1$ $mathrm{mod} 2$ - parity.
Is there any similar name for the remainder for any other base? Like a generalization of parity? Could I use parity in a broader sense, just to name the remainder $mathrm{mod} n$?
elementary-number-theory soft-question integers
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
$endgroup$
We have a name for the property of integers to be $0$ or $1$ $mathrm{mod} 2$ - parity.
Is there any similar name for the remainder for any other base? Like a generalization of parity? Could I use parity in a broader sense, just to name the remainder $mathrm{mod} n$?
elementary-number-theory soft-question integers
elementary-number-theory soft-question integers
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
asked Feb 25 at 11:34
dEmigOddEmigOd
1,5411612
1,5411612
9
$begingroup$
How about congruence?
$endgroup$
– Umberto P.
Feb 25 at 11:37
$begingroup$
So should I say (variable)'s congruence class or value?
$endgroup$
– dEmigOd
Feb 25 at 11:43
$begingroup$
I had the same question and thought about terminology for $n = 3$. A friend of mine came up with a very neat suggestion: flat, short and long. I don't know if there is any other generalization, but I would very much like to hear people talking about remainders mod 3 like this. I guess the reason why this has a name for $n=2$ is that it appears commonly in everyday life as opposed to most of the other numbers. When talking about time, the 12 is dropped at all, but this is somewhat different maybe
$endgroup$
– kesa
Feb 25 at 15:44
add a comment |
9
$begingroup$
How about congruence?
$endgroup$
– Umberto P.
Feb 25 at 11:37
$begingroup$
So should I say (variable)'s congruence class or value?
$endgroup$
– dEmigOd
Feb 25 at 11:43
$begingroup$
I had the same question and thought about terminology for $n = 3$. A friend of mine came up with a very neat suggestion: flat, short and long. I don't know if there is any other generalization, but I would very much like to hear people talking about remainders mod 3 like this. I guess the reason why this has a name for $n=2$ is that it appears commonly in everyday life as opposed to most of the other numbers. When talking about time, the 12 is dropped at all, but this is somewhat different maybe
$endgroup$
– kesa
Feb 25 at 15:44
9
9
$begingroup$
How about congruence?
$endgroup$
– Umberto P.
Feb 25 at 11:37
$begingroup$
How about congruence?
$endgroup$
– Umberto P.
Feb 25 at 11:37
$begingroup$
So should I say (variable)'s congruence class or value?
$endgroup$
– dEmigOd
Feb 25 at 11:43
$begingroup$
So should I say (variable)'s congruence class or value?
$endgroup$
– dEmigOd
Feb 25 at 11:43
$begingroup$
I had the same question and thought about terminology for $n = 3$. A friend of mine came up with a very neat suggestion: flat, short and long. I don't know if there is any other generalization, but I would very much like to hear people talking about remainders mod 3 like this. I guess the reason why this has a name for $n=2$ is that it appears commonly in everyday life as opposed to most of the other numbers. When talking about time, the 12 is dropped at all, but this is somewhat different maybe
$endgroup$
– kesa
Feb 25 at 15:44
$begingroup$
I had the same question and thought about terminology for $n = 3$. A friend of mine came up with a very neat suggestion: flat, short and long. I don't know if there is any other generalization, but I would very much like to hear people talking about remainders mod 3 like this. I guess the reason why this has a name for $n=2$ is that it appears commonly in everyday life as opposed to most of the other numbers. When talking about time, the 12 is dropped at all, but this is somewhat different maybe
$endgroup$
– kesa
Feb 25 at 15:44
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
Simply say "congruent to $a$ modulo $m$" to read "$equiv a pmod{m}$".
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
$endgroup$
add a comment |
$begingroup$
Actually there is a standard name: residue.
There are $5$ residues modulo $5$, namely $0,1,2,3,4$.
Every prime greater than $3$ falls into only $2$ residue-classes modulo $6$.
answered Feb 25 at 15:56
user21820user21820
39.3k543154
$endgroup$
add a comment |
$begingroup$
In a broader sense, when you are dealing with congruences you are dealing with an equivalence relation and its equivalence classes.
The basic idea of an equivalence relation is to collect elements that are different but behave in the same manner with respect to some property of interest.
In modular arithmetic this property is having the same rest when divided by a prescribed integer
If $a=bbmod m$ or $aequiv_m b$ you essentially say that $a$ and $b$ are in the same equivalence class with respect to the equivalence relation $equiv_m$.
So you could say that "$a$ and $b$ are in the same equivalence class when we look at the remainder upon dividing by $m$", which definitely longer and more cumbersome to say "$a$ congruent to $b$ modulo $m$" but nonetheless another way to express the same concept.
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
$endgroup$
add a comment |
$begingroup$
Either AlessioDV's good answer, or you could say: "of the form $nq+r$". as a representation of $equiv r pmod n$ for example a number $N$ with $$Nequiv 1pmod 3$$ has property $N=3q+1$.
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
$endgroup$
add a comment |
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Simply say "congruent to $a$ modulo $m$" to read "$equiv a pmod{m}$".
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
$endgroup$
add a comment |
$begingroup$
Simply say "congruent to $a$ modulo $m$" to read "$equiv a pmod{m}$".
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
$endgroup$
add a comment |
$begingroup$
Simply say "congruent to $a$ modulo $m$" to read "$equiv a pmod{m}$".
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
$endgroup$
Simply say "congruent to $a$ modulo $m$" to read "$equiv a pmod{m}$".
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
answered Feb 25 at 11:39
AlessioDVAlessioDV
667114
667114
add a comment |
add a comment |
$begingroup$
Actually there is a standard name: residue.
There are $5$ residues modulo $5$, namely $0,1,2,3,4$.
Every prime greater than $3$ falls into only $2$ residue-classes modulo $6$.
answered Feb 25 at 15:56
user21820user21820
39.3k543154
$endgroup$
add a comment |
$begingroup$
Actually there is a standard name: residue.
There are $5$ residues modulo $5$, namely $0,1,2,3,4$.
Every prime greater than $3$ falls into only $2$ residue-classes modulo $6$.
answered Feb 25 at 15:56
user21820user21820
39.3k543154
$endgroup$
add a comment |
$begingroup$
Actually there is a standard name: residue.
There are $5$ residues modulo $5$, namely $0,1,2,3,4$.
Every prime greater than $3$ falls into only $2$ residue-classes modulo $6$.
answered Feb 25 at 15:56
user21820user21820
39.3k543154
$endgroup$
Actually there is a standard name: residue.
There are $5$ residues modulo $5$, namely $0,1,2,3,4$.
Every prime greater than $3$ falls into only $2$ residue-classes modulo $6$.
answered Feb 25 at 15:56
user21820user21820
39.3k543154
answered Feb 25 at 15:56
user21820user21820
39.3k543154
answered Feb 25 at 15:56
user21820user21820
39.3k543154
answered Feb 25 at 15:56
user21820user21820
39.3k543154
39.3k543154
add a comment |
add a comment |
$begingroup$
In a broader sense, when you are dealing with congruences you are dealing with an equivalence relation and its equivalence classes.
The basic idea of an equivalence relation is to collect elements that are different but behave in the same manner with respect to some property of interest.
In modular arithmetic this property is having the same rest when divided by a prescribed integer
If $a=bbmod m$ or $aequiv_m b$ you essentially say that $a$ and $b$ are in the same equivalence class with respect to the equivalence relation $equiv_m$.
So you could say that "$a$ and $b$ are in the same equivalence class when we look at the remainder upon dividing by $m$", which definitely longer and more cumbersome to say "$a$ congruent to $b$ modulo $m$" but nonetheless another way to express the same concept.
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
$endgroup$
add a comment |
$begingroup$
In a broader sense, when you are dealing with congruences you are dealing with an equivalence relation and its equivalence classes.
The basic idea of an equivalence relation is to collect elements that are different but behave in the same manner with respect to some property of interest.
In modular arithmetic this property is having the same rest when divided by a prescribed integer
If $a=bbmod m$ or $aequiv_m b$ you essentially say that $a$ and $b$ are in the same equivalence class with respect to the equivalence relation $equiv_m$.
So you could say that "$a$ and $b$ are in the same equivalence class when we look at the remainder upon dividing by $m$", which definitely longer and more cumbersome to say "$a$ congruent to $b$ modulo $m$" but nonetheless another way to express the same concept.
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
$endgroup$
add a comment |
$begingroup$
In a broader sense, when you are dealing with congruences you are dealing with an equivalence relation and its equivalence classes.
The basic idea of an equivalence relation is to collect elements that are different but behave in the same manner with respect to some property of interest.
In modular arithmetic this property is having the same rest when divided by a prescribed integer
If $a=bbmod m$ or $aequiv_m b$ you essentially say that $a$ and $b$ are in the same equivalence class with respect to the equivalence relation $equiv_m$.
So you could say that "$a$ and $b$ are in the same equivalence class when we look at the remainder upon dividing by $m$", which definitely longer and more cumbersome to say "$a$ congruent to $b$ modulo $m$" but nonetheless another way to express the same concept.
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
$endgroup$
In a broader sense, when you are dealing with congruences you are dealing with an equivalence relation and its equivalence classes.
The basic idea of an equivalence relation is to collect elements that are different but behave in the same manner with respect to some property of interest.
In modular arithmetic this property is having the same rest when divided by a prescribed integer
If $a=bbmod m$ or $aequiv_m b$ you essentially say that $a$ and $b$ are in the same equivalence class with respect to the equivalence relation $equiv_m$.
So you could say that "$a$ and $b$ are in the same equivalence class when we look at the remainder upon dividing by $m$", which definitely longer and more cumbersome to say "$a$ congruent to $b$ modulo $m$" but nonetheless another way to express the same concept.
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
edited Feb 25 at 14:53
J. W. Tanner
2,6861217
2,6861217
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
answered Feb 25 at 11:52
Vinyl_coat_jawaVinyl_coat_jawa
3,20511233
3,20511233
add a comment |
add a comment |
$begingroup$
Either AlessioDV's good answer, or you could say: "of the form $nq+r$". as a representation of $equiv r pmod n$ for example a number $N$ with $$Nequiv 1pmod 3$$ has property $N=3q+1$.
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
$endgroup$
add a comment |
$begingroup$
Either AlessioDV's good answer, or you could say: "of the form $nq+r$". as a representation of $equiv r pmod n$ for example a number $N$ with $$Nequiv 1pmod 3$$ has property $N=3q+1$.
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
$endgroup$
add a comment |
$begingroup$
Either AlessioDV's good answer, or you could say: "of the form $nq+r$". as a representation of $equiv r pmod n$ for example a number $N$ with $$Nequiv 1pmod 3$$ has property $N=3q+1$.
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
$endgroup$
Either AlessioDV's good answer, or you could say: "of the form $nq+r$". as a representation of $equiv r pmod n$ for example a number $N$ with $$Nequiv 1pmod 3$$ has property $N=3q+1$.
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
answered Feb 25 at 11:49
Rhys HughesRhys Hughes
6,9571530
6,9571530
add a comment |
add a comment |
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9
$begingroup$
How about congruence?
$endgroup$
– Umberto P.
Feb 25 at 11:37
$begingroup$
So should I say (variable)'s congruence class or value?
$endgroup$
– dEmigOd
Feb 25 at 11:43
$begingroup$
I had the same question and thought about terminology for $n = 3$. A friend of mine came up with a very neat suggestion: flat, short and long. I don't know if there is any other generalization, but I would very much like to hear people talking about remainders mod 3 like this. I guess the reason why this has a name for $n=2$ is that it appears commonly in everyday life as opposed to most of the other numbers. When talking about time, the 12 is dropped at all, but this is somewhat different maybe
$endgroup$
– kesa
Feb 25 at 15:44