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$f(x,y)=(x/2^y) mod 16$ a Bivariate function?
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I have a two-input function on the integers or naturals. Is a bivariate function a function that takes two inputs or is there anything more to it?
For example take the function:
$f(x,y)=(x/2^y) mod 16$
where $f:mathbb{N}tomathbb{N}$ or $mathbb{Z^+}tomathbb{Z^+}$, $x$ and $y in mathbb{N}$ or $mathbb{Z^+}$.
Is $f(x,y)$ called a bivariate function?
Does it have other names or is this the only description for such a function?
functions terminology integers natural-numbers
asked 2 days ago
Natural Number Guy
442415
add a comment |
up vote
0
down vote
favorite
I have a two-input function on the integers or naturals. Is a bivariate function a function that takes two inputs or is there anything more to it?
For example take the function:
$f(x,y)=(x/2^y) mod 16$
where $f:mathbb{N}tomathbb{N}$ or $mathbb{Z^+}tomathbb{Z^+}$, $x$ and $y in mathbb{N}$ or $mathbb{Z^+}$.
Is $f(x,y)$ called a bivariate function?
Does it have other names or is this the only description for such a function?
functions terminology integers natural-numbers
asked 2 days ago
Natural Number Guy
442415
$2$ does not have a multiplicative inverse modulo $16$ so $frac {1}{2}$ doesn't have a meaning.
– Doug M
2 days ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a two-input function on the integers or naturals. Is a bivariate function a function that takes two inputs or is there anything more to it?
For example take the function:
$f(x,y)=(x/2^y) mod 16$
where $f:mathbb{N}tomathbb{N}$ or $mathbb{Z^+}tomathbb{Z^+}$, $x$ and $y in mathbb{N}$ or $mathbb{Z^+}$.
Is $f(x,y)$ called a bivariate function?
Does it have other names or is this the only description for such a function?
functions terminology integers natural-numbers
asked 2 days ago
Natural Number Guy
442415
I have a two-input function on the integers or naturals. Is a bivariate function a function that takes two inputs or is there anything more to it?
For example take the function:
$f(x,y)=(x/2^y) mod 16$
where $f:mathbb{N}tomathbb{N}$ or $mathbb{Z^+}tomathbb{Z^+}$, $x$ and $y in mathbb{N}$ or $mathbb{Z^+}$.
Is $f(x,y)$ called a bivariate function?
Does it have other names or is this the only description for such a function?
functions terminology integers natural-numbers
functions terminology integers natural-numbers
asked 2 days ago
Natural Number Guy
442415
asked 2 days ago
Natural Number Guy
442415
asked 2 days ago
Natural Number Guy
442415
asked 2 days ago
Natural Number Guy
442415
asked 2 days ago
Natural Number Guy
442415
442415
$2$ does not have a multiplicative inverse modulo $16$ so $frac {1}{2}$ doesn't have a meaning.
– Doug M
2 days ago
add a comment |
$2$ does not have a multiplicative inverse modulo $16$ so $frac {1}{2}$ doesn't have a meaning.
– Doug M
2 days ago
$2$ does not have a multiplicative inverse modulo $16$ so $frac {1}{2}$ doesn't have a meaning.
– Doug M
2 days ago
$2$ does not have a multiplicative inverse modulo $16$ so $frac {1}{2}$ doesn't have a meaning.
– Doug M
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
I've learned my math in American English and I would call that function "binary", or "a function of two variables". "Bivariate" does get used in statistics, with a meaning that is similar to the way you're using it, but it's subtly different and I think you're more likely to confuse people if you use it here.
Your notation $f : mathbb{N} rightarrow mathbb{N}$ is not correct. You should write $f : mathbb{N} times mathbb{N} rightarrow mathbb{N}$, and likewise for $mathbb{Z}^+$. If you talk to computer programmers, especially Haskell programmers, they will disagree with this notation, but it is correct when doing math.
You do have another problem lurking in your statement, though, in that your function, as written, doesn't seem to map into the naturals all the time. For instance $$f(69,2) = (69/4 mod 16) = (17 tfrac{1}{4} mod 16)$$ I don't think there's a universally agreed understanding of what the $mod()$ function should do for non-interger inputs. You could choose to have it equal $ 1 tfrac{1}{4}$, in which case $f : mathbb{N} times mathbb{N} rightarrow mathbb{Q}$, or you could truncate the fraction part, and have it equal $1$, but you'd need to change your definition to specify that.
Response to comments:
Math doesn't really use the concept of "integer division"; that's more of a computer programming thing. We tend to use the "floor" function, aka "greatest integer less than or equal to", aka "drop the fractional part", aka "truncate", which is written $lfloor x rfloor$. So you would write $$ text{Consider } f:mathbb{N} times mathbb{N} rightarrow mathbb{N} text{ given by } f(x,y) = lfloor x/2^y rfloor mod 16.$$
You don't really need to mention that $f$ is binary -- it's obvious from the way it's written. You might mention it if you were comparing it to functions that take more arguments, in which case the word you would use is "arity".
answered 2 days ago
JonathanZ
2,022613
How do I define that the mod function should only take integer inputs? Also I forgot to say that the division is an integer division, also how do I define or describe that in the text, meaning that both the numerator, denominator and result of the operation is integer?
– Natural Number Guy
2 days ago
@NaturalNumberGuy - response added to answer.
– JonathanZ
2 days ago
That answered my question
– Natural Number Guy
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
I've learned my math in American English and I would call that function "binary", or "a function of two variables". "Bivariate" does get used in statistics, with a meaning that is similar to the way you're using it, but it's subtly different and I think you're more likely to confuse people if you use it here.
Your notation $f : mathbb{N} rightarrow mathbb{N}$ is not correct. You should write $f : mathbb{N} times mathbb{N} rightarrow mathbb{N}$, and likewise for $mathbb{Z}^+$. If you talk to computer programmers, especially Haskell programmers, they will disagree with this notation, but it is correct when doing math.
You do have another problem lurking in your statement, though, in that your function, as written, doesn't seem to map into the naturals all the time. For instance $$f(69,2) = (69/4 mod 16) = (17 tfrac{1}{4} mod 16)$$ I don't think there's a universally agreed understanding of what the $mod()$ function should do for non-interger inputs. You could choose to have it equal $ 1 tfrac{1}{4}$, in which case $f : mathbb{N} times mathbb{N} rightarrow mathbb{Q}$, or you could truncate the fraction part, and have it equal $1$, but you'd need to change your definition to specify that.
Response to comments:
Math doesn't really use the concept of "integer division"; that's more of a computer programming thing. We tend to use the "floor" function, aka "greatest integer less than or equal to", aka "drop the fractional part", aka "truncate", which is written $lfloor x rfloor$. So you would write $$ text{Consider } f:mathbb{N} times mathbb{N} rightarrow mathbb{N} text{ given by } f(x,y) = lfloor x/2^y rfloor mod 16.$$
You don't really need to mention that $f$ is binary -- it's obvious from the way it's written. You might mention it if you were comparing it to functions that take more arguments, in which case the word you would use is "arity".
answered 2 days ago
JonathanZ
2,022613
How do I define that the mod function should only take integer inputs? Also I forgot to say that the division is an integer division, also how do I define or describe that in the text, meaning that both the numerator, denominator and result of the operation is integer?
– Natural Number Guy
2 days ago
@NaturalNumberGuy - response added to answer.
– JonathanZ
2 days ago
That answered my question
– Natural Number Guy
2 days ago
add a comment |
up vote
0
down vote
accepted
I've learned my math in American English and I would call that function "binary", or "a function of two variables". "Bivariate" does get used in statistics, with a meaning that is similar to the way you're using it, but it's subtly different and I think you're more likely to confuse people if you use it here.
Your notation $f : mathbb{N} rightarrow mathbb{N}$ is not correct. You should write $f : mathbb{N} times mathbb{N} rightarrow mathbb{N}$, and likewise for $mathbb{Z}^+$. If you talk to computer programmers, especially Haskell programmers, they will disagree with this notation, but it is correct when doing math.
You do have another problem lurking in your statement, though, in that your function, as written, doesn't seem to map into the naturals all the time. For instance $$f(69,2) = (69/4 mod 16) = (17 tfrac{1}{4} mod 16)$$ I don't think there's a universally agreed understanding of what the $mod()$ function should do for non-interger inputs. You could choose to have it equal $ 1 tfrac{1}{4}$, in which case $f : mathbb{N} times mathbb{N} rightarrow mathbb{Q}$, or you could truncate the fraction part, and have it equal $1$, but you'd need to change your definition to specify that.
Response to comments:
Math doesn't really use the concept of "integer division"; that's more of a computer programming thing. We tend to use the "floor" function, aka "greatest integer less than or equal to", aka "drop the fractional part", aka "truncate", which is written $lfloor x rfloor$. So you would write $$ text{Consider } f:mathbb{N} times mathbb{N} rightarrow mathbb{N} text{ given by } f(x,y) = lfloor x/2^y rfloor mod 16.$$
You don't really need to mention that $f$ is binary -- it's obvious from the way it's written. You might mention it if you were comparing it to functions that take more arguments, in which case the word you would use is "arity".
answered 2 days ago
JonathanZ
2,022613
How do I define that the mod function should only take integer inputs? Also I forgot to say that the division is an integer division, also how do I define or describe that in the text, meaning that both the numerator, denominator and result of the operation is integer?
– Natural Number Guy
2 days ago
@NaturalNumberGuy - response added to answer.
– JonathanZ
2 days ago
That answered my question
– Natural Number Guy
2 days ago
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
I've learned my math in American English and I would call that function "binary", or "a function of two variables". "Bivariate" does get used in statistics, with a meaning that is similar to the way you're using it, but it's subtly different and I think you're more likely to confuse people if you use it here.
Your notation $f : mathbb{N} rightarrow mathbb{N}$ is not correct. You should write $f : mathbb{N} times mathbb{N} rightarrow mathbb{N}$, and likewise for $mathbb{Z}^+$. If you talk to computer programmers, especially Haskell programmers, they will disagree with this notation, but it is correct when doing math.
You do have another problem lurking in your statement, though, in that your function, as written, doesn't seem to map into the naturals all the time. For instance $$f(69,2) = (69/4 mod 16) = (17 tfrac{1}{4} mod 16)$$ I don't think there's a universally agreed understanding of what the $mod()$ function should do for non-interger inputs. You could choose to have it equal $ 1 tfrac{1}{4}$, in which case $f : mathbb{N} times mathbb{N} rightarrow mathbb{Q}$, or you could truncate the fraction part, and have it equal $1$, but you'd need to change your definition to specify that.
Response to comments:
Math doesn't really use the concept of "integer division"; that's more of a computer programming thing. We tend to use the "floor" function, aka "greatest integer less than or equal to", aka "drop the fractional part", aka "truncate", which is written $lfloor x rfloor$. So you would write $$ text{Consider } f:mathbb{N} times mathbb{N} rightarrow mathbb{N} text{ given by } f(x,y) = lfloor x/2^y rfloor mod 16.$$
You don't really need to mention that $f$ is binary -- it's obvious from the way it's written. You might mention it if you were comparing it to functions that take more arguments, in which case the word you would use is "arity".
answered 2 days ago
JonathanZ
2,022613
I've learned my math in American English and I would call that function "binary", or "a function of two variables". "Bivariate" does get used in statistics, with a meaning that is similar to the way you're using it, but it's subtly different and I think you're more likely to confuse people if you use it here.
Your notation $f : mathbb{N} rightarrow mathbb{N}$ is not correct. You should write $f : mathbb{N} times mathbb{N} rightarrow mathbb{N}$, and likewise for $mathbb{Z}^+$. If you talk to computer programmers, especially Haskell programmers, they will disagree with this notation, but it is correct when doing math.
You do have another problem lurking in your statement, though, in that your function, as written, doesn't seem to map into the naturals all the time. For instance $$f(69,2) = (69/4 mod 16) = (17 tfrac{1}{4} mod 16)$$ I don't think there's a universally agreed understanding of what the $mod()$ function should do for non-interger inputs. You could choose to have it equal $ 1 tfrac{1}{4}$, in which case $f : mathbb{N} times mathbb{N} rightarrow mathbb{Q}$, or you could truncate the fraction part, and have it equal $1$, but you'd need to change your definition to specify that.
Response to comments:
Math doesn't really use the concept of "integer division"; that's more of a computer programming thing. We tend to use the "floor" function, aka "greatest integer less than or equal to", aka "drop the fractional part", aka "truncate", which is written $lfloor x rfloor$. So you would write $$ text{Consider } f:mathbb{N} times mathbb{N} rightarrow mathbb{N} text{ given by } f(x,y) = lfloor x/2^y rfloor mod 16.$$
You don't really need to mention that $f$ is binary -- it's obvious from the way it's written. You might mention it if you were comparing it to functions that take more arguments, in which case the word you would use is "arity".
answered 2 days ago
JonathanZ
2,022613
edited 2 days ago
answered 2 days ago
JonathanZ
2,022613
answered 2 days ago
JonathanZ
2,022613
answered 2 days ago
JonathanZ
2,022613
2,022613
How do I define that the mod function should only take integer inputs? Also I forgot to say that the division is an integer division, also how do I define or describe that in the text, meaning that both the numerator, denominator and result of the operation is integer?
– Natural Number Guy
2 days ago
@NaturalNumberGuy - response added to answer.
– JonathanZ
2 days ago
That answered my question
– Natural Number Guy
2 days ago
add a comment |
How do I define that the mod function should only take integer inputs? Also I forgot to say that the division is an integer division, also how do I define or describe that in the text, meaning that both the numerator, denominator and result of the operation is integer?
– Natural Number Guy
2 days ago
@NaturalNumberGuy - response added to answer.
– JonathanZ
2 days ago
That answered my question
– Natural Number Guy
2 days ago
How do I define that the mod function should only take integer inputs? Also I forgot to say that the division is an integer division, also how do I define or describe that in the text, meaning that both the numerator, denominator and result of the operation is integer?
– Natural Number Guy
2 days ago
How do I define that the mod function should only take integer inputs? Also I forgot to say that the division is an integer division, also how do I define or describe that in the text, meaning that both the numerator, denominator and result of the operation is integer?
– Natural Number Guy
2 days ago
@NaturalNumberGuy - response added to answer.
– JonathanZ
2 days ago
@NaturalNumberGuy - response added to answer.
– JonathanZ
2 days ago
That answered my question
– Natural Number Guy
2 days ago
That answered my question
– Natural Number Guy
2 days ago
add a comment |
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$2$ does not have a multiplicative inverse modulo $16$ so $frac {1}{2}$ doesn't have a meaning.
– Doug M
2 days ago