What is the meaning of := in mathematical notation?

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The notation "u := -v" indicates that u is defined to be the negative of v, where v has been previously established. This use of ":=" is common in mathematical contexts to clarify definitions. It is often encountered in advanced topics, such as Fourier Transforms, where precise variable definitions are crucial. Additionally, software like MathCad utilizes this notation for defining variables and functions. Overall, ":=" serves as a clear way to communicate the relationship between variables in mathematical expressions.
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u := -v

specifically the " := "

Here is the context. When f, g are suitably regular functions on R we can use the change of variable u:=-v etc..I should add that I came across this in a Fourier Transform book..

Thanks!
 
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It usually means 'defined to be'.

So in this context, we know what v is, and we want to define u as a new variable. So you write u := -v to let the reader know u is being defined as -v (where v has been defined previously).
 
Ah... well that makes sense
thank you very much.
 
What, you haven't learned all half-dozen (dozen?) different symbols for "defined as" yet? :p
 
the program MathCad uses the ":=" to define things like variables and functions. perhaps you saw a document made with mathcad?
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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