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September 7th, 2015, 12:41 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, 01:14 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,768 Thanks: 699 
See answer in physics forums.

September 7th, 2015, 03:20 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
You should give a link so the rest of us can find it! https://www.physicsforums.com/threads/whatdoesthetermpointwisereferto.831356/ Last edited by skipjack; September 8th, 2015 at 04:49 PM. 
September 7th, 2015, 08:27 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
In the specified context, the word "pointwise" is redundant.

September 8th, 2015, 01:24 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,156 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
I haven't encountered "pointwise" much, but I have encountered "piecewise". I think pointwise makes sense once you've read about piecewise things 
September 8th, 2015, 04:09 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,768 Thanks: 699 
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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