# cut and paste and exchange argument difference?

In a graph $\mathcal G=(V, E)$ let $a,z \in V$

For proving the shortest distance from $a$ to $z$:

• We have a sub path $i$ to $j$ such that $a\rightarrow i \rightarrow j \rightarrow z$ If we find a smaller.
• Sub path $i'\rightarrow j'$ such that $ai'j'z < aijz$.
• We say that to prove $a\rightarrow z$ is the shortest path we have to prove it's sub-path has a shortest path.

Is this proof by cut and paste or exchange argument? Or are they both same ?

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 That's the first time I hear about these proof techniques ("cut and paste" and "exchange argument"). The terminology isn't standard, so you can call the proof whatever name you want. – Yuval Filmus Dec 10 '12 at 20:40