Proving multiplication floor functions












0












$begingroup$


If x, y is bigger than zero (I mean real numbers bigger than 0.) Then why does this always works?
[x][y]<=[xy]<([x]+1)([y]+1)



<= means less or equal to
brackets are floor function










share|cite|improve this question









$endgroup$












  • $begingroup$
    Please use MathJax to format your posts.
    $endgroup$
    – saulspatz
    Jan 13 at 1:39










  • $begingroup$
    I am sorry but I don't know how to use it
    $endgroup$
    – mathhero
    Jan 13 at 1:40






  • 3




    $begingroup$
    Write $x=n+delta, y=m+varepsilon,$ where $m,n$ are nonnegative integers, and $0ledelta,varepsilon<1.$
    $endgroup$
    – saulspatz
    Jan 13 at 1:41






  • 1




    $begingroup$
    That's why I gave you a link to the tutorial. It's not hard.
    $endgroup$
    – saulspatz
    Jan 13 at 1:42
















0












$begingroup$


If x, y is bigger than zero (I mean real numbers bigger than 0.) Then why does this always works?
[x][y]<=[xy]<([x]+1)([y]+1)



<= means less or equal to
brackets are floor function










share|cite|improve this question









$endgroup$












  • $begingroup$
    Please use MathJax to format your posts.
    $endgroup$
    – saulspatz
    Jan 13 at 1:39










  • $begingroup$
    I am sorry but I don't know how to use it
    $endgroup$
    – mathhero
    Jan 13 at 1:40






  • 3




    $begingroup$
    Write $x=n+delta, y=m+varepsilon,$ where $m,n$ are nonnegative integers, and $0ledelta,varepsilon<1.$
    $endgroup$
    – saulspatz
    Jan 13 at 1:41






  • 1




    $begingroup$
    That's why I gave you a link to the tutorial. It's not hard.
    $endgroup$
    – saulspatz
    Jan 13 at 1:42














0












0








0





$begingroup$


If x, y is bigger than zero (I mean real numbers bigger than 0.) Then why does this always works?
[x][y]<=[xy]<([x]+1)([y]+1)



<= means less or equal to
brackets are floor function










share|cite|improve this question









$endgroup$




If x, y is bigger than zero (I mean real numbers bigger than 0.) Then why does this always works?
[x][y]<=[xy]<([x]+1)([y]+1)



<= means less or equal to
brackets are floor function







proof-verification inequality floor-function






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 13 at 0:50









mathheromathhero

235




235












  • $begingroup$
    Please use MathJax to format your posts.
    $endgroup$
    – saulspatz
    Jan 13 at 1:39










  • $begingroup$
    I am sorry but I don't know how to use it
    $endgroup$
    – mathhero
    Jan 13 at 1:40






  • 3




    $begingroup$
    Write $x=n+delta, y=m+varepsilon,$ where $m,n$ are nonnegative integers, and $0ledelta,varepsilon<1.$
    $endgroup$
    – saulspatz
    Jan 13 at 1:41






  • 1




    $begingroup$
    That's why I gave you a link to the tutorial. It's not hard.
    $endgroup$
    – saulspatz
    Jan 13 at 1:42


















  • $begingroup$
    Please use MathJax to format your posts.
    $endgroup$
    – saulspatz
    Jan 13 at 1:39










  • $begingroup$
    I am sorry but I don't know how to use it
    $endgroup$
    – mathhero
    Jan 13 at 1:40






  • 3




    $begingroup$
    Write $x=n+delta, y=m+varepsilon,$ where $m,n$ are nonnegative integers, and $0ledelta,varepsilon<1.$
    $endgroup$
    – saulspatz
    Jan 13 at 1:41






  • 1




    $begingroup$
    That's why I gave you a link to the tutorial. It's not hard.
    $endgroup$
    – saulspatz
    Jan 13 at 1:42
















$begingroup$
Please use MathJax to format your posts.
$endgroup$
– saulspatz
Jan 13 at 1:39




$begingroup$
Please use MathJax to format your posts.
$endgroup$
– saulspatz
Jan 13 at 1:39












$begingroup$
I am sorry but I don't know how to use it
$endgroup$
– mathhero
Jan 13 at 1:40




$begingroup$
I am sorry but I don't know how to use it
$endgroup$
– mathhero
Jan 13 at 1:40




3




3




$begingroup$
Write $x=n+delta, y=m+varepsilon,$ where $m,n$ are nonnegative integers, and $0ledelta,varepsilon<1.$
$endgroup$
– saulspatz
Jan 13 at 1:41




$begingroup$
Write $x=n+delta, y=m+varepsilon,$ where $m,n$ are nonnegative integers, and $0ledelta,varepsilon<1.$
$endgroup$
– saulspatz
Jan 13 at 1:41




1




1




$begingroup$
That's why I gave you a link to the tutorial. It's not hard.
$endgroup$
– saulspatz
Jan 13 at 1:42




$begingroup$
That's why I gave you a link to the tutorial. It's not hard.
$endgroup$
– saulspatz
Jan 13 at 1:42










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