How do I prove $ lfloor f(n) rfloor approx f(n), forall f:N rightarrow R$? The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Prove that $lfloorlfloor x/2 rfloor / 2 rfloor = lfloor x/4 rfloor$Prove that $lfloor an rfloor +lfloor (1-a)n rfloor = n-1 $Evaluate $lfloor fracxm rfloor + lfloor fracx+1m rfloor + dots + lfloor fracx+m-1m rfloor $Prove that $leftlfloor lfloor x/2rfloor/2 rightrfloor=lfloor x/4rfloor$ for all $x$.Writting a proof for $lfloor 4x rfloor = lfloor x+1/4 rfloor + lfloor x+1/2 rfloor + lfloor x+3/4 rfloor + lfloor x rfloor$$lfloor sqrtlceil x rceil rfloor = lfloor sqrtx rfloor, forall x in mathbbR$For all $x$ which are real numbers, prove that $lfloor 2xrfloor = lfloor xrfloor + lfloor x+0.5rfloor.$Give a proof by cases that $lfloor 4x rfloor = lfloor x rfloor + lfloor x+0.25 rfloor + lfloor x+0.5 rfloor + lfloor x+0.75 rfloor$$left lfloor log_bx right rfloor = left lfloor log_bleft lfloor x right rfloor right rfloor$Values for which $lfloor x/y rfloor = biglfloor lfloor x rfloor / lfloor y rfloor bigrfloor$
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How do I prove $ lfloor f(n) rfloor approx f(n), forall f:N rightarrow R$?
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Prove that $lfloorlfloor x/2 rfloor / 2 rfloor = lfloor x/4 rfloor$Prove that $lfloor an rfloor +lfloor (1-a)n rfloor = n-1 $Evaluate $lfloor fracxm rfloor + lfloor fracx+1m rfloor + dots + lfloor fracx+m-1m rfloor $Prove that $leftlfloor lfloor x/2rfloor/2 rightrfloor=lfloor x/4rfloor$ for all $x$.Writting a proof for $lfloor 4x rfloor = lfloor x+1/4 rfloor + lfloor x+1/2 rfloor + lfloor x+3/4 rfloor + lfloor x rfloor$$lfloor sqrtlceil x rceil rfloor = lfloor sqrtx rfloor, forall x in mathbbR$For all $x$ which are real numbers, prove that $lfloor 2xrfloor = lfloor xrfloor + lfloor x+0.5rfloor.$Give a proof by cases that $lfloor 4x rfloor = lfloor x rfloor + lfloor x+0.25 rfloor + lfloor x+0.5 rfloor + lfloor x+0.75 rfloor$$left lfloor log_bx right rfloor = left lfloor log_bleft lfloor x right rfloor right rfloor$Values for which $lfloor x/y rfloor = biglfloor lfloor x rfloor / lfloor y rfloor bigrfloor$
$begingroup$
How do I prove $ lfloor f(n) rfloor approx f(n), forall f:N rightarrow R$? It seems pretty intuitive, but I haven't found a way to express it mathematically.
This question comes from the discrete mathematics course I'm taking, and I believe we're supposed to use the definition of $a(x) approx b(x)$ as $a(x) = b(x)(1+varepsilon(x))$, where $limlimits_x to infty varepsilon(x) = 0$.
I couldn't find this or a similar proof (searched the textbook, google and stackexchange).
discrete-mathematics
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
$endgroup$
add a comment |
$begingroup$
How do I prove $ lfloor f(n) rfloor approx f(n), forall f:N rightarrow R$? It seems pretty intuitive, but I haven't found a way to express it mathematically.
This question comes from the discrete mathematics course I'm taking, and I believe we're supposed to use the definition of $a(x) approx b(x)$ as $a(x) = b(x)(1+varepsilon(x))$, where $limlimits_x to infty varepsilon(x) = 0$.
I couldn't find this or a similar proof (searched the textbook, google and stackexchange).
discrete-mathematics
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
$endgroup$
1
$begingroup$
$f(n)=1.5$ for every $n$ seems to be not true.
$endgroup$
– Mann
Mar 31 at 15:15
$begingroup$
Sorry, I don't know what you mean by $f(n)+f(n)$. $lfloor f(n) rfloor$ is defined as the biggest integer that is less or equal than $f(n)$ ($f(n)-1 < lfloor f(n) rfloor leq f(n)$)
$endgroup$
– Raul Almeida
Mar 31 at 15:15
$begingroup$
$lfloor f(n)rfloor+leftf(n)right=f(n)$, it's basically saying that $f(n)$ is the sum of it's "integer part" and "fractional part"
$endgroup$
– Mann
Mar 31 at 15:16
1
$begingroup$
I've been trying to make it true for $f(n)=1.5 forall n$ but it seems to not be. Thank you.
$endgroup$
– Raul Almeida
Mar 31 at 15:46
$begingroup$
Maybe the statement is for fucntions which diverges for large $n$. Take the cases when $lim_n to infty f(n) = infty$
$endgroup$
– Mann
Mar 31 at 15:48
add a comment |
$begingroup$
How do I prove $ lfloor f(n) rfloor approx f(n), forall f:N rightarrow R$? It seems pretty intuitive, but I haven't found a way to express it mathematically.
This question comes from the discrete mathematics course I'm taking, and I believe we're supposed to use the definition of $a(x) approx b(x)$ as $a(x) = b(x)(1+varepsilon(x))$, where $limlimits_x to infty varepsilon(x) = 0$.
I couldn't find this or a similar proof (searched the textbook, google and stackexchange).
discrete-mathematics
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
$endgroup$
How do I prove $ lfloor f(n) rfloor approx f(n), forall f:N rightarrow R$? It seems pretty intuitive, but I haven't found a way to express it mathematically.
This question comes from the discrete mathematics course I'm taking, and I believe we're supposed to use the definition of $a(x) approx b(x)$ as $a(x) = b(x)(1+varepsilon(x))$, where $limlimits_x to infty varepsilon(x) = 0$.
I couldn't find this or a similar proof (searched the textbook, google and stackexchange).
discrete-mathematics
discrete-mathematics
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
asked Mar 31 at 14:50
Raul AlmeidaRaul Almeida
213
213
1
$begingroup$
$f(n)=1.5$ for every $n$ seems to be not true.
$endgroup$
– Mann
Mar 31 at 15:15
$begingroup$
Sorry, I don't know what you mean by $f(n)+f(n)$. $lfloor f(n) rfloor$ is defined as the biggest integer that is less or equal than $f(n)$ ($f(n)-1 < lfloor f(n) rfloor leq f(n)$)
$endgroup$
– Raul Almeida
Mar 31 at 15:15
$begingroup$
$lfloor f(n)rfloor+leftf(n)right=f(n)$, it's basically saying that $f(n)$ is the sum of it's "integer part" and "fractional part"
$endgroup$
– Mann
Mar 31 at 15:16
1
$begingroup$
I've been trying to make it true for $f(n)=1.5 forall n$ but it seems to not be. Thank you.
$endgroup$
– Raul Almeida
Mar 31 at 15:46
$begingroup$
Maybe the statement is for fucntions which diverges for large $n$. Take the cases when $lim_n to infty f(n) = infty$
$endgroup$
– Mann
Mar 31 at 15:48
add a comment |
1
$begingroup$
$f(n)=1.5$ for every $n$ seems to be not true.
$endgroup$
– Mann
Mar 31 at 15:15
$begingroup$
Sorry, I don't know what you mean by $f(n)+f(n)$. $lfloor f(n) rfloor$ is defined as the biggest integer that is less or equal than $f(n)$ ($f(n)-1 < lfloor f(n) rfloor leq f(n)$)
$endgroup$
– Raul Almeida
Mar 31 at 15:15
$begingroup$
$lfloor f(n)rfloor+leftf(n)right=f(n)$, it's basically saying that $f(n)$ is the sum of it's "integer part" and "fractional part"
$endgroup$
– Mann
Mar 31 at 15:16
1
$begingroup$
I've been trying to make it true for $f(n)=1.5 forall n$ but it seems to not be. Thank you.
$endgroup$
– Raul Almeida
Mar 31 at 15:46
$begingroup$
Maybe the statement is for fucntions which diverges for large $n$. Take the cases when $lim_n to infty f(n) = infty$
$endgroup$
– Mann
Mar 31 at 15:48
1
1
$begingroup$
$f(n)=1.5$ for every $n$ seems to be not true.
$endgroup$
– Mann
Mar 31 at 15:15
$begingroup$
$f(n)=1.5$ for every $n$ seems to be not true.
$endgroup$
– Mann
Mar 31 at 15:15
$begingroup$
Sorry, I don't know what you mean by $f(n)+f(n)$. $lfloor f(n) rfloor$ is defined as the biggest integer that is less or equal than $f(n)$ ($f(n)-1 < lfloor f(n) rfloor leq f(n)$)
$endgroup$
– Raul Almeida
Mar 31 at 15:15
$begingroup$
Sorry, I don't know what you mean by $f(n)+f(n)$. $lfloor f(n) rfloor$ is defined as the biggest integer that is less or equal than $f(n)$ ($f(n)-1 < lfloor f(n) rfloor leq f(n)$)
$endgroup$
– Raul Almeida
Mar 31 at 15:15
$begingroup$
$lfloor f(n)rfloor+leftf(n)right=f(n)$, it's basically saying that $f(n)$ is the sum of it's "integer part" and "fractional part"
$endgroup$
– Mann
Mar 31 at 15:16
$begingroup$
$lfloor f(n)rfloor+leftf(n)right=f(n)$, it's basically saying that $f(n)$ is the sum of it's "integer part" and "fractional part"
$endgroup$
– Mann
Mar 31 at 15:16
1
1
$begingroup$
I've been trying to make it true for $f(n)=1.5 forall n$ but it seems to not be. Thank you.
$endgroup$
– Raul Almeida
Mar 31 at 15:46
$begingroup$
I've been trying to make it true for $f(n)=1.5 forall n$ but it seems to not be. Thank you.
$endgroup$
– Raul Almeida
Mar 31 at 15:46
$begingroup$
Maybe the statement is for fucntions which diverges for large $n$. Take the cases when $lim_n to infty f(n) = infty$
$endgroup$
– Mann
Mar 31 at 15:48
$begingroup$
Maybe the statement is for fucntions which diverges for large $n$. Take the cases when $lim_n to infty f(n) = infty$
$endgroup$
– Mann
Mar 31 at 15:48
add a comment |
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1
$begingroup$
$f(n)=1.5$ for every $n$ seems to be not true.
$endgroup$
– Mann
Mar 31 at 15:15
$begingroup$
Sorry, I don't know what you mean by $f(n)+f(n)$. $lfloor f(n) rfloor$ is defined as the biggest integer that is less or equal than $f(n)$ ($f(n)-1 < lfloor f(n) rfloor leq f(n)$)
$endgroup$
– Raul Almeida
Mar 31 at 15:15
$begingroup$
$lfloor f(n)rfloor+leftf(n)right=f(n)$, it's basically saying that $f(n)$ is the sum of it's "integer part" and "fractional part"
$endgroup$
– Mann
Mar 31 at 15:16
1
$begingroup$
I've been trying to make it true for $f(n)=1.5 forall n$ but it seems to not be. Thank you.
$endgroup$
– Raul Almeida
Mar 31 at 15:46
$begingroup$
Maybe the statement is for fucntions which diverges for large $n$. Take the cases when $lim_n to infty f(n) = infty$
$endgroup$
– Mann
Mar 31 at 15:48