Discrete maths

[grizzled forge]

I don’t understand this proof can someone help me understand it

[deft elk]

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[dark jacinth]

To prove that $f$ is onto, you need to prove that $\forall y \in \mathbb{Z},\exists x \in \mathbb{Z}$ such that $f(x) = y$. Because all $y \in \mathbb{Z}$ must have at least 1 antecedent with $f$.

[left yacht]

Yojda

[dark jacinth]

The proof above take a $b$ arbitrary, and find an $x$ such that $f(x) = b$. Ohh, we know that $b-1 \in \mathbb{Z}$ (we have to check that before), and $f(b-1) = b$. So we found $x = b-1$ such that $f(x) = b$. And because we took $b$ arbitrary, that means $\forall b \in \mathbb{Z}, f(b-1) = b$.

[left yacht]

Yojda