Let f : N `to N : f(x) =2 x` for all `x in N`
Show that f is one -one and into.

Explanation

To show that the function \( f : \mathbb{N} \to \mathbb{N} \) defined by \( f(x) = 2x \) is one-one (injective) and into (not onto), we will follow these steps:

### Step 1: Show that \( f \) is one-one

To prove that \( f \) is one-one, we need to show that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

1. Assume \( f(x_1) = f(x_2) \).
2. This means \( 2x_1 = 2x_2 \).
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