Understanding the Invariance of Hamming Distance: A Shift Proof

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florenti
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Please help me ...

to show that the Hamming disatance d(x,y) is invariant to a shift of both x and y i.e

d(x+z, y+z)=d(x,y)

Thanks a lot

flo
 
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florenti said:
Please help me ...

to show that the Hamming disatance d(x,y) is invariant to a shift of both x and y i.e

d(x+z, y+z)=d(x,y)

Thanks a lot

flo

Another poster, Lenti, asked this same question a couple of days ago.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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