How do you prove : |a|≥ a
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How do you prove : |a|≥ a

[From: ] [author: ] [Date: 11-11-12] [Hit: ]
then a = |a|.therefore absolute value of a is bigger than or equal to a-The absolute value ensures that a will be a positive number. If a is positive to begin with, then |a|=a. If a was negative to begin with then |a|>a. Hope that helps!......
How do you prove a|≥ a ?

Thanks.

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If a ≥ 0, then a = |a|.

If a < 0, then 0 < -a. So a < -a and -a = |a|. Hence a < |a|.

Since either a ≥ 0 or a < 0, then |a| ≥ a.

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the absolute value of a can only be positive where as (a) can either ( -a) or (a)
the absolute value of a is bigger than -a and equal to a
therefore absolute value of a is bigger than or equal to a

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The absolute value ensures that a will be a positive number. If a is positive to begin with, then |a|=a. If a was negative to begin with then |a|>a. Hope that helps!
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