Analysis of information sources in references of the Wikipedia article "Big O notation" in English language version.
Because θ(g(n)) is a set, we could write "f(n) ∈ θ(g(n))" to indicate that f(n) is a member of θ(g(n)). Instead, we will usually write f(n) = θ(g(n)) to express the same notion. You might be confused because we abuse equality in this way, but we shall see later in this section that doing so has its advantages.
When the asymptotic notation stands alone (that is, not within a larger formula) on the right-hand side of an equation (or inequality), as in n = O(n2), we have already defined the equal sign to mean set membership: n ∈ O(n2). In general, however, when asymptotic notation appears in a formula, we interpret it as standing for some anonymous function that we do not care to name. For example, the formula 2n2 + 3n + 1 = 2n2 + θ(n) means that 2n2 + 3n + 1 = 2n2 + f(n), where f(n) is some function in the set θ(n). In this case, we let f(n) = 3n + 1, which is indeed in θ(n). Using asymptotic notation in this manner can help eliminate inessential detail and clutter in an equation.
