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 Post subject: inequality proofPosted: Sat, 21 May 2011 16:31:21 UTC
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Joined: Thu, 23 Sep 2010 10:34:44 UTC
Posts: 32
With reference to Bartle and Sherbert Introduction to Real Analysis Pg 28 Example 2.1.13

May I know how to proof this?

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 Post subject: Re: inequality proofPosted: Sat, 21 May 2011 17:01:28 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
symbian wrote:
With reference to Bartle and Sherbert Introduction to Real Analysis Pg 28 Example 2.1.13

May I know how to proof this?

by positivity of a and b.

Similarly the square root follows from the first one with new a being the old and new b being old .

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 Post subject: Re: inequality proofPosted: Thu, 15 Sep 2011 22:29:33 UTC
 S.O.S. Oldtimer

Joined: Mon, 28 Dec 2009 00:16:28 UTC
Posts: 228
Let x and y be positive numbers. If x ≤ y, then √x ≤ √y.

Proof. Suppose x ≤ y.
Subtracting y from both sides gives x - y ≤ 0 ⇔ (√x)^2 - (√y)^2 ≤ 0.
Factor this to get (√x - √y)(√x + √y) ≤ 0.
Dividing both sides by the positive number √x + √y produces √x - √y ≤ 0.
Adding √y to both sides gives √x ≤ √y.

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