0

My professor wants me to write the proof method of every proof at the beginning. Something of the form

$\textbf{proof. }\textit{[proof method.]} \\ [\text{body}] \\ [\text{conclusion}] \\ \square$

What do I call my method if I use something like the AM-GM inequality or absolute value identities? Are those still direct proofs? Or are they indirect proofs? My understanding right now is if I use facts/assumptions pertaining to the proposition, then it's a direct proof. For example, showing if $a|b$ and $b|c$ then $a|c$ by showing that by substitution $c=aln$ for integers $l,n$, therefore $a|c$. Otherwise its an indirect proof. I'm not too sure about the semantic differences overall though.

Lex_i
  • 2,072
  • 10
  • 26
  • First you need an exact list of proof methods, which have a well-defined name, and have appeared in your lecture. – Dietrich Burde Feb 10 '21 at 15:59
  • 1
    The simplest distinction is a direct proof which directly goes from premise to conclusion using direct deductions entirely from the premises, and indirect proof, which involves an assumption so that you may derive a contradiction. – While I Am Feb 10 '21 at 16:07

0 Answers0