It looks like you’re asking about the meaning of “$inj” in a mathematical context. Most likely, this is shorthand for “injective”, which is a property of functions. Let me explain carefully.
Injective Function
A function is injective (or one-to-one) if different inputs map to different outputs. Formally:
f \text{ is injective} \quad \iff \quad \forall x_1, x_2 \in A, \ f(x_1) = f(x_2) \implies x_1 = x_2
Equivalently:
No two distinct elements in the domain have the same image.
Every element of the codomain is mapped by at most one element of the domain.
Example 1
Suppose . Then . ✅
So is injective.
Example 2
but . ❌
So is not injective.
In some texts, you might see or , meaning “f is injective”.
