What is the meaning of := in mathematical notation?

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Discussion Overview

The discussion centers around the meaning of the notation ":=" in mathematical contexts, particularly in relation to defining variables and functions. Participants explore its usage in different scenarios, including its appearance in a Fourier Transform book and software like MathCad.

Discussion Character

  • Conceptual clarification, Technical explanation, Meta-discussion

Main Points Raised

  • One participant presents the notation u := -v and seeks clarification on its meaning.
  • Another participant explains that ":=" typically means 'defined to be', indicating that u is being defined in terms of v.
  • A third participant expresses understanding and appreciation for the explanation provided.
  • One participant humorously notes the existence of multiple symbols for "defined as," suggesting a variety of notational conventions.
  • Another participant mentions that MathCad uses ":=" for defining variables and functions, implying that this might be a source of confusion for some users.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of ":=" as a definition, but there is acknowledgment of the existence of multiple notational conventions, which may lead to differing perspectives.

Contextual Notes

Some assumptions about the familiarity with mathematical notation and software tools are present, but these are not explicitly stated or resolved in the discussion.

BustedBreaks
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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?
 

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