Equal to by definition

It means “is defined as.” In A ≝ B, B gives the definition of A; the sign introduces a convention instead of reporting a result proved later.

The order carries meaning: the expression on the left is the one being named, so switching sides can change the statement.

Definition signs took several forms

A historical account reports a double-equality form for “equal by definition” in 1920; other forms include =₍Def₎, :=, ≡, and related marks.

The purpose is to give an expression a precise name or shorthand. By 1958, ALGOL-era programming used := as a definition or assignment convention, while mathematical writing continued to choose among forms.

Should I write ≝ or :=?

Follow the convention your field already uses. ≝ is legible in mathematical writing, while := is familiar in many programming and technical contexts.

If readers may not know the sign, write “defined as” the first time. The document’s house style determines which notation readers will recognize quickly.