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September 7th, 2015, 12:41 PM   #1
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What does the term "pointwise" refer to?

In reading mathematical texts (especially on functions), I come across the term "pointwise". There seems to be a paucity of information explaining it on the internet, so I turn to the forum for an intuitive explanation. The context is when the term is used as in "pointwise addition" or "pointwise multiplication" of functions.
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September 7th, 2015, 01:14 PM   #2
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See answer in physics forums.
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September 7th, 2015, 03:20 PM   #3
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You should give a link so the rest of us can find it!

Last edited by skipjack; September 8th, 2015 at 04:49 PM.
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September 7th, 2015, 08:27 PM   #4
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In the specified context, the word "pointwise" is redundant.
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September 8th, 2015, 01:24 AM   #5
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I haven't encountered "point-wise" much, but I have encountered "piece-wise". I think point-wise makes sense once you've read about piece-wise things
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September 8th, 2015, 04:09 PM   #6
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I apologize for leaving out reference. To repeat - let f and g be functions, then pointwise addition f+g means f(x)+g(x) for every x in the domain. I also added a comment that the concept of pointwise is used more ofter in the context of taking limits.

$\displaystyle f_n-> f\ pointwise,\ means \ f_n(x)->f(x) \ for\ each\ x$.

There are many other kinds of convergence, so it is important to state what one means in context.
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