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Show that the function f: N->N , given b...

Show that the function `f: N->N` , given by `f(x)=2x` , is one-one but not onto.

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To show that the function \( f: \mathbb{N} \to \mathbb{N} \) defined by \( f(x) = 2x \) is one-one but not onto, we will analyze the function step by step. ### Step 1: Show that the function is one-one (injective) To prove that the function 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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