My Math Forum What does the term "pointwise" refer to?

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 September 7th, 2015, 01:41 PM #1 Senior Member     Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus 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.
 September 7th, 2015, 02:14 PM #2 Global Moderator   Joined: May 2007 Posts: 6,679 Thanks: 658 See answer in physics forums.
 September 7th, 2015, 04:20 PM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 You should give a link so the rest of us can find it! https://www.physicsforums.com/threads/what-does-the-term-pointwise-refer-to.831356/ Last edited by skipjack; September 8th, 2015 at 05:49 PM.
 September 7th, 2015, 09:27 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,262 Thanks: 1958 In the specified context, the word "pointwise" is redundant.
 September 8th, 2015, 02:24 AM #5 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,134 Thanks: 720 Math Focus: Physics, mathematical modelling, numerical and computational solutions 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
 September 8th, 2015, 05:09 PM #6 Global Moderator   Joined: May 2007 Posts: 6,679 Thanks: 658 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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