things to say in proofs instead of “trivially”




  • Obviously
  • Clearly
  • The proof is left to the reader that
  • We all agree that
  • I would wager 5 dollars that
  • By the Axiom of Choice
  • With p < 0.05, we conclude that
  • By the Laws of Mathematics
  • If you’ve been paying attention you’d realize that
  • Terry Tao told me in a personal email that
  • The voices insist that
  • Somebody once told me



The following snippet may prove useful:

  {Trivially, }
  {Obviously, }
  {The proof is left to the reader that }
  {We all agree that }
  {We assume without loss of generality that }
  {We assume without any good reason that }
  {Any undergraduate could see that }
  {It's probably true that }
  {I bet you can't disprove that }
  {I would wager 5 dollars that }
  {I would wager two and half cows that }
  {\pgfmathrandominteger{\a}{2}{50000} I would wager .\a \leavevmode\vtop{\offinterlineskip
    \setbox2=\hbox to\wd0{\hfil\hskip-.03em
    \vrule height .3ex width .15ex\hskip .08em
    \vrule height .3ex width .15ex\hfil}
    \vbox{\copy2\box0}\box2} that }
  {By the Axiom of Choice, }
  {By the Laws of Mathematics, }
  {By the power vested in me by the State of Massachusetts, }
  {By the Hammer of Grabthar, }
  {According to the IMU, }
  {According to Ada Lovelace, }
  {According to Hoyle, }
  {According to this book I found (I can't remember the name but I think it had a sort of vapor-wave cover? It might've been blue? I think the author's name had an m in it somewhere, or possibly a g?), }
  {In accordance with the Prophecy, }
  {With p $<$ 0.05 we conclude that }
  {If you'd been paying attention you'd have already realized that }
  {Terry Tao told me in a personal email that }
  {The ghost of Paul Erd\H{o}s told me via Ouija board that }
  {A voice in a dream told me that }
  {The voices insist that }
  {As Srinivasa Ramanujan once said, }
  {In the words of Emmy Noether, }
  {As Dwayne "The Rock" Johnson said in his groundbreaking treatise \textit{1001 fun facts and formul\ae}, }
  {$\twonotes\;\textit{Somebody once told me}\;\twonotes$ that }

See also: ways to end proofs

Also @twocubes. I had to use the HTML editor to get it to format properly, and I couldn’t figure out how to tag people from there.