Proof by Construction

Example

Prove the following: $\exists x\in \mathbb{Z}$ s.t. (such that) $x>2$ and $x^2-5x+6>0$

1. Let $x=17$
2. Note that $17\in \mathbb{Z}$ and $17>2$
3. Also, $x^2-5x+6=210>0$

Notes

• Proof by construction is where you explicitly find the value with the correct properties
• It is a form of Direct Proof
• No need to explain how you found the result (e.g. 17), you just need to show that the result has the required properties