A function f: A → B is said to be injective (or one-to-one) if for every a1, a2 in A, if f(a1) = f(a2), then a1 = a2.

Here are the steps to prove a function is injective:

1. Assume that f(a1) = f(a2) for some a1, a2 in A. This is our assumption.

2. Substitute these into the function definition to get two equations.

3. If from these equations, we can deduce that a1 = a2, then the function is injective.

4. If we cannot deduce that a1 = a2, then the function is not injective.

Remember, the key property of an injective

Question

A function f: A → B is said to be injective (or one-to-one) if for every a1, a2 in A, if f(a1) = f(a2), then a1 = a2.

Here are the steps to prove a function is injective:

1. Assume that f(a1) = f(a2) for some a1, a2 in A. This is our assumption.

2. Substitute these into the function definition to get two equations.

3. If from these equations, we can deduce that a1 = a2, then the function is injective.

4. If we cannot deduce that a1 = a2, then the function is not injective.

Remember, the key property of an injective

Knowee AI · Accepted Answer

A function f: A → B is said to be injective (or one-to-one) if for every a1, a2 in A, if f(a1) = f(a2), then a1 = a2.

Here are the steps to prove a function is injective:

1. Assume that f(a1) = f(a2) for some a1, a2 in A. This is our assumption.

2. Substitute these into the function definition to get two equations.

3. If from these equations, we can deduce that a1 = a2, then the function is injective.

4. If we cannot deduce that a1 = a2, then the function is not injective.

Remember, the key property of an injective

function f : A → B is injective i