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- Thread starter jason177
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if f = g+ h is continuous it certainly doesn't imply that g and h are continuous as well. For example, try g(x ) = 1 if x is irrational and g(x ) = 0 if x is rational -- then set h to be vice versa, g + h will be a constant function ( with the constant 1 ) but it is clear that neither g and h are continuous everywhere

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