# What does := mean?

What does := mean?

It is borrowed from computer programming: it means that the item on the left hand side is being defined to be what is on the right hand side. For example,

means that $y$ is defined to be $7x+2$.

This is different from, say, writing

where we are saying that the two sides are equal, but we are not defining “1” to be the expression “$\sin^2(\theta) + \cos^2(\theta)$“.

Basically, some people think that there should be notational difference between saying “I define blah to be equal to blankety” and saying “blah is equal to blankety“. So they use := for the first and = for the latter. Usually, it is clear from context which of the two uses of the equal sign is intended (often because of signal words like “Let”, “We define”, etc.)