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Dick said:Well, yes. Just interchanging the order just interchanges increasing/decreasing and signs. It doesn't make any real difference to the problem. But ##|s_n(x) - s(x)|## is still increasing as a function of x on [0,1]. Not decreasing. It's an absolute value. I'm still not sure you are clear on what's important and what is not.
Oh so It doesn't make any difference at all. I see now.
It's just |a-b| = |b-a| looked wrong to me for a moment ( Can't even explain why). Now that that's clear I think I'm good.