Wikipedia: History of Absolute value

Difference (from prior major revision) (author diff)

Changed: 4c4

# |a| ≥ 0

Changed: 7,10c7,11

# |a+b| ≤ |a| + |b|
# |a-b| ≥ ||a| - |b||
# it can be expressed: |a| = √ (a²)
# For a > 0, |x| ≤ a if and only if -a ≤ x ≤ a

# |a/b| = |a| / |b| (if b ≠ 0)
# |a+b| ≤ |a| + |b|
# |a-b| ≥ ||a| - |b||
# |a| = √ (a²)
# |a| ≤ b if and only if -b ≤ a ≤ b

Changed: 21c22

For a complex number z = a + ib, one defines the absolute value or modulus to be |z| = √ (a² + b²) = √ (z z^*). This notion of absolute value shares the properties 1-5 from above. If one interprets z as a point in the plane, then |z| is the distance of z to the origin.

For a complex number z = a + ib, one defines the absolute value or modulus to be |z| = √ (a² + b²) = √ (z z^*). This notion of absolute value shares the properties 1-6 from above. If one interprets z as a point in the plane, then |z| is the distance of z to the origin.

	Revision 20 . . November 28, 2001 6:57 am by AxelBoldt
	Revision 19 . . (edit) November 11, 2001 2:43 am by AxelBoldt
	Revision 18 . . November 11, 2001 2:24 am by (logged).123.179.xxx *[fixed a formatting problem.]**