What is the Meaning of ##:=## in Mathematics?

[Von Neumann]

My calc professor always used to use the symbol $:=$ when defining a quantity.

For example, say we want to evaluate the integral $\int x \sqrt{1+x^2} dx$. So we might say, "Let $u:=1+x^2$" and then continue to easily evaluate the integral.

I haven't seen this anywhere else and I'm wondering if this is standard notation.

 

[WannabeNewton]

It is standard notation yes. It usually denotes "defined as" or "definition"

 

[micromass]

Yes, it's standard notation. It's not the only notation people use though. But you'll see some people use it.

The use of this notation in papers and math books is discouraged though. It's always better to write it out in words. For the same reason, things like $\forall$ and $\exists$ rarely show up in math texts.

But many people use it informally or on blackboard.

 

[DeIdeal]

Yes. I've seen several alternatives, such as $\equiv$, $\stackrel{\Delta}{=}$ and $\stackrel{\mathrm{def}}{=}$, but using $:=$ is also extremely common.

I'm not sure if this is just me, but it seems to be more common in a slightly informal presentation.

EDIT: Double-ninja'd, ugh.

 

[WannabeNewton]

Ninja powah!

 

[Von Neumann]

Thanks fellas!