# Math Proof

Prove that for all integers n > or = 1 and all real numbers x subscript 1, x subscript 2,...., x subscript n. absolute value of (x subscript 1+ x subscript 2+...+ x subscript n) <or= abs(x subscript 1) + abs( x subscript 2)+..+ abs(x subscript n)

I know how to do the triangle inequality where I just have 2 values in the reals. But I don't understand how to generalize it to more than 2 values in the reals.

1. 👍 0
2. 👎 0
3. 👁 161
1. we want to show that

|x1 + x2 + ... + xn| <= |x1| + |x2| + ... + |xn|

Let's take n=3

We know that the inequality holds for n=2, so now we have

|(x1+x2)+x3| <= |(x1+x2)| + |x3|
But, we already know that |x1+x2| <= |x1|+|x2|, so we now have

|x1+x2+x3| <= |x1|+|x2|+|x3|
as was desired.

You can see that using the associative property of real numbers extends the proof to any positive integer n.

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### Algebra

Order the following numbers from least to greatest. √5, -0.1, (-5/3), 0.7, √2 a. 0.7, √2, (-5/3), √5, -0.1 b. √5, √2, 0.7, (-5/3), -0.1 c. (-5/3), -0.1, 0.7, √2, √5 ? d. -0.1, 0.7, √2, √5, (-5/3) To which

asked by Anonymous on September 21, 2013
2. ### Math

Which set of best describes the numbers used on a scale for a standard thermometer? A.whole numbers B.rational numbers C.real numbers D.integers I choose Real Numbers if I am incorrect can you explain why.

asked by Olivia on May 10, 2015
3. ### Algebra

To which subset of real numbers does the following number belong? square root of 7 A)rational numbers B)irrational numbers****** C)whole numbers, integers, rational numbers D)whole numbers, natural numbers, integers

asked by Trish on September 4, 2015
4. ### Math help Ms. Sue please

1. Name the subset(s) of real numbers to which the number zero belongs. You can choose more than one answer. Irrational numbers Integers Whole numbers Natural numbers 2. Write an algebraic expression for the word phrase: the

asked by Charlotte on September 10, 2013
5. ### CHEMISTRY

I am having trouble balancing this equation: Ca(OH){subscript 2} + (NH{subscript 4}){subscript 2} SO{subscript 4} -> CaSO{subscript 4} + NH{subscript 3} + H{subscript 2} O Please help, thanks. Response Ca(OH)2 + (NH4)2SO4 -->

asked by Anonymous on October 13, 2008
6. ### Chemistry

Calculate the amount (g) of each of the following salts that need to be added to a 200 mL volumetric flask to produce a 2 M solution of S. CaSO(subscript 4) [NH(subscript 4)subscript 2]SO(subscript 4) NOTE: the subscript 2 is

asked by Sejul on January 19, 2013
7. ### math

describe the solutions of 4

asked by es on January 8, 2013
8. ### Math 115 #20

Label each statement as true or false a. All integers are real numbers. b. All negative integers are whole numbers. c. Zero is neither positive nor negative. d. All integers are whole numbers. I think all answera are TRUE am I

asked by Deb on January 9, 2009
9. ### CHEMISTRY

Here's one last equation I can't balance: Al{subscript 2}(SO{subscript 4}){subscript 3} + ZnCl{subscript 2} -> AlCl{subscript 3} + ZnSO{subscript 4} Please help, and thanks again. Response Al2(SO4)3 + 3ZnCl2 ---> 2AlCl3 +

asked by Anonymous on October 13, 2008
10. ### CHEMISTRY

Here's one last equation I can't balance: Al{subscript 2}(SO{subscript 4}){subscript 3} + ZnCl{subscript 2} -> AlCl{subscript 3} + ZnSO{subscript 4} Please help, and thanks again. Responses Al2(SO4)3 + 3ZnCl2 ---> 2AlCl3 +

asked by Anonymous on October 13, 2008

More Similar Questions