- #1

yxgao

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The answer is d^(1/2)

How do you prove this mathematically?

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- Thread starter yxgao
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- #1

yxgao

- 123

- 0

The answer is d^(1/2)

How do you prove this mathematically?

- #2

NateTG

Science Advisor

Homework Helper

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[tex]d(a,b) = 0 \iff a=b[/tex]

(which is easy in this case)

[tex]d(a,b) \geq 0[/tex]

(also easy)

[tex]d(a,c) \leq d(a,b)+d(b,c)[/tex]

Which is the only one that really needs any looking into in this case.

The does not necessarily hold for [tex]d'=d^2[/tex] since if you have [tex]d(a,b)=1[/tex] and [tex]d(b,c)=1[/tex] and [tex]d(a,b)=2[/tex], then the triangle inequality does not hold for [tex]d'[/tex].

To prove that the triangle inequality holds for [tex]d'=d^{\frac{1}{2}}[/tex], start with the triangle inequality for [tex]d[/tex], complete the square on the RHS, and take the square root of both sides.

- #3

yxgao

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that makes perfect sense.

thanks

thanks

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