# Negative of Integer

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## Theorem

Let $x \in \Z$ be an integer.

Let $x = \eqclass {a, b} {}$ be defined from the formal definition of integers, where $\eqclass {a, b} {}$ is an equivalence class of ordered pairs of natural numbers.

Then:

- $-x = \eqclass {b, a} {}$

## Proof

Follows from Inverse for Integer Addition.

This needs considerable tedious hard slog to complete it.In particular: The whole area of construction of integers from the inverse completion needs to be reviewedTo discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Finish}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |