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So, as the question asks, is we have only normalised floating-point values and normalised results, could you please explain how x + y = x?

I know it all relates to precision, but how can I explain that?

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    I would suggest that you look up what machine epsilon is first, and then we can talk.2011-05-01

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Suppose you have a floating-point system which keeps track of, say, two decimal digits. If $x=1.0 \times 10^0$ and $y=3.4 \times 10^{-10}$, then the exact value of $x+y$ is $1.00000000034$, which would be represented in your system by the closest floating-point number, which is... Well, what is it?

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    how to prove it in general for any $x,y$ with $|y|ps\times \beta^{-1}\times |x|$? – 2014-04-18