Definition of modulus function
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Good day.
I'm an A-Level student and I've recently learnt about the modulus operation. Based on both wikipedia and my A-Level textbook, for $xlt 0, |x|= -x$.
However, since $0 = -0, |0| = -0$ and thus when $x = 0, |x| = -x$. Therefore, shouldn't the definition of the modulus function be : for $xleq 0, |x| = -x$?
Reference: https://en.wikipedia.org/wiki/Absolute_value
real-numbers
edited Dec 1 at 4:54
Thomas Shelby
804115
asked Dec 1 at 4:13
Robin Ting
94
add a comment |
up vote
0
down vote
favorite
Good day.
I'm an A-Level student and I've recently learnt about the modulus operation. Based on both wikipedia and my A-Level textbook, for $xlt 0, |x|= -x$.
However, since $0 = -0, |0| = -0$ and thus when $x = 0, |x| = -x$. Therefore, shouldn't the definition of the modulus function be : for $xleq 0, |x| = -x$?
Reference: https://en.wikipedia.org/wiki/Absolute_value
real-numbers
edited Dec 1 at 4:54
Thomas Shelby
804115
asked Dec 1 at 4:13
Robin Ting
94
1
$0=-0$ means the definition can go either way, but $|x|=x:x=0$ is easier, and $|0|=0$ is easier still. What benefits would your proposed definition provide, and how do they supersede the simplicity of the conventional definition?
– Nij
Dec 1 at 4:19
$atimes 0=0forall ainmathbb{R}$
– Sujit Bhattacharyya
Dec 1 at 4:31
Just thought that |x| = -x when x ≤ 0 would be a more accurate definition for the case where |x| = -x
– Robin Ting
Dec 1 at 4:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Good day.
I'm an A-Level student and I've recently learnt about the modulus operation. Based on both wikipedia and my A-Level textbook, for $xlt 0, |x|= -x$.
However, since $0 = -0, |0| = -0$ and thus when $x = 0, |x| = -x$. Therefore, shouldn't the definition of the modulus function be : for $xleq 0, |x| = -x$?
Reference: https://en.wikipedia.org/wiki/Absolute_value
real-numbers
edited Dec 1 at 4:54
Thomas Shelby
804115
asked Dec 1 at 4:13
Robin Ting
94
Good day.
I'm an A-Level student and I've recently learnt about the modulus operation. Based on both wikipedia and my A-Level textbook, for $xlt 0, |x|= -x$.
However, since $0 = -0, |0| = -0$ and thus when $x = 0, |x| = -x$. Therefore, shouldn't the definition of the modulus function be : for $xleq 0, |x| = -x$?
Reference: https://en.wikipedia.org/wiki/Absolute_value
real-numbers
real-numbers
edited Dec 1 at 4:54
Thomas Shelby
804115
asked Dec 1 at 4:13
Robin Ting
94
edited Dec 1 at 4:54
Thomas Shelby
804115
asked Dec 1 at 4:13
Robin Ting
94
edited Dec 1 at 4:54
Thomas Shelby
804115
edited Dec 1 at 4:54
Thomas Shelby
804115
edited Dec 1 at 4:54
Thomas Shelby
804115
804115
asked Dec 1 at 4:13
Robin Ting
94
asked Dec 1 at 4:13
Robin Ting
94
asked Dec 1 at 4:13
Robin Ting
94
94
1
$0=-0$ means the definition can go either way, but $|x|=x:x=0$ is easier, and $|0|=0$ is easier still. What benefits would your proposed definition provide, and how do they supersede the simplicity of the conventional definition?
– Nij
Dec 1 at 4:19
$atimes 0=0forall ainmathbb{R}$
– Sujit Bhattacharyya
Dec 1 at 4:31
Just thought that |x| = -x when x ≤ 0 would be a more accurate definition for the case where |x| = -x
– Robin Ting
Dec 1 at 4:53
add a comment |
1
$0=-0$ means the definition can go either way, but $|x|=x:x=0$ is easier, and $|0|=0$ is easier still. What benefits would your proposed definition provide, and how do they supersede the simplicity of the conventional definition?
– Nij
Dec 1 at 4:19
$atimes 0=0forall ainmathbb{R}$
– Sujit Bhattacharyya
Dec 1 at 4:31
Just thought that |x| = -x when x ≤ 0 would be a more accurate definition for the case where |x| = -x
– Robin Ting
Dec 1 at 4:53
1
1
$0=-0$ means the definition can go either way, but $|x|=x:x=0$ is easier, and $|0|=0$ is easier still. What benefits would your proposed definition provide, and how do they supersede the simplicity of the conventional definition?
– Nij
Dec 1 at 4:19
$0=-0$ means the definition can go either way, but $|x|=x:x=0$ is easier, and $|0|=0$ is easier still. What benefits would your proposed definition provide, and how do they supersede the simplicity of the conventional definition?
– Nij
Dec 1 at 4:19
$atimes 0=0forall ainmathbb{R}$
– Sujit Bhattacharyya
Dec 1 at 4:31
$atimes 0=0forall ainmathbb{R}$
– Sujit Bhattacharyya
Dec 1 at 4:31
Just thought that |x| = -x when x ≤ 0 would be a more accurate definition for the case where |x| = -x
– Robin Ting
Dec 1 at 4:53
Just thought that |x| = -x when x ≤ 0 would be a more accurate definition for the case where |x| = -x
– Robin Ting
Dec 1 at 4:53
add a comment |
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1
$0=-0$ means the definition can go either way, but $|x|=x:x=0$ is easier, and $|0|=0$ is easier still. What benefits would your proposed definition provide, and how do they supersede the simplicity of the conventional definition?
– Nij
Dec 1 at 4:19
$atimes 0=0forall ainmathbb{R}$
– Sujit Bhattacharyya
Dec 1 at 4:31
Just thought that |x| = -x when x ≤ 0 would be a more accurate definition for the case where |x| = -x
– Robin Ting
Dec 1 at 4:53