On "def" notation

Asked Jan 21 '22 at 08:59

Active Jan 21 '22 at 08:59

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I've been perplexed by the notation of writing def above an equal sign, even though it seems rather trivial. So, in the example below, is this the correct usage of def?

$f'(x) \stackrel{\text{def}}{=} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Also, is this notation preferred to $:=$?

asked Jan 21 '22 at 08:59

Alexander

5

Yes it is correct and common. "Preferred" is subjective. I use $:=$ because it is easier to typeset. – Jan 21 '22 at 09:07
1

The "equality" sign has many uses (and meanings)... – Mauro ALLEGRANZA Jan 21 '22 at 09:14
1

See also this post – Mauro ALLEGRANZA Jan 21 '22 at 09:16
(You may also see $\overset{def}{\iff}$ used similarly.) – Milten Jan 21 '22 at 18:05

On "def" notation

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