LAFl[àÄÆîî’ˆùÔ ObviouslyÔClearlyÔAnyone can see thatÔ TriviallyÔIndubitablyÔIt follows thatÔ EvidentlyÔ2By basic applications of previously proven lemmas,Ô$The proof is left to the reader thatÔIt goes without saying thatÔConsequentlyÔBy immediate consequence,Ô Of courseÔBut then againÔBy symmetryÔWithout loss of generality,Ô0Anyone with a fifth grade education can see thatÔI would wager 5 dollars thatÔBy the contrapositiveÔ%We need not waste ink in proving thatÔBy EulerÔ By FermatÔ%By a simple diagonalization argument,ÔWe all agree thatÔIt would be absurd to deny thatÔUnquestionably,Ô
Indisputably,ÔIt is plain to see thatÔ.It would be embarrassing to miss the fact thatÔ8It would be an insult to my time and yours to prove thatÔ+Any cretin with half a brain could see thatÔBy Fermatâ€™s Last Theorem,ÔBy the Axiom of Choice,Ô/It is equivalent to the Riemann Hypothesis thatÔBy a simple counting argument,ÔSimply put,Ô5Oneâ€™s mind immediately leaps to the conclusion thatÔBy contradiction,Ô3I shudder to think of the poor soul who denies thatÔ2It is readily apparent to the casual observer thatÔWith p < 5% we conclude thatÔ0It follows from the Zermelo-Fraenkel axioms thatÔSet theory tells us thatÔ%Divine inspiration reveals to us thatÔ Patently,ÔNeedless to say,ÔBy logicÔBy the Laws of MathematicsÔ
By all means,ÔWith probability 1,ÔWho could deny thatÔ"Assuming the Continuum Hypothesis,Ô$Galois died in order to show us thatÔBThere is a marvellous proof (which is too long to write here) thatÔWe proved in class thatÔ4Our friends over at Harvard recently discovered thatÔ"It is straightforward to show thatÔBy definition,ÔBy a simple assumption,ÔIt is easy to see thatÔ"Even you would be able to see thatÔEverybody knows thatÔ)I donâ€™t know why anybody would ask, butÔBetween you and me,Ô4Unless you accept GÃ¶delâ€™s Incompleteness Theorem,ÔA reliable source has told meÔ0It is a matter of simple arithmetic to show thatÔBeyond a shadow of a doubt,ÔhWhen we view this problem as an undecidable residue class whose elements are universal DAGs, we see thatÔYou and I both know thatÔAnd there you have it,ÔAnd as easy as ABC,ÔAnd then as quick as a wink,Ô6If youâ€™ve been paying attention youâ€™d realize thatÔBy the Pigeonhole PrincipleÔ!By circular reasoning we see thatÔ6When we make the necessary and sufficient assumptions,Ô3It is beyond the scope of this course to prove thatÔ3Only idealogues and sycophants would debate whetherÔ9It is an unfortunately common misconception to doubt thatÔ$By petitio principii, we assert thatÔWe may take for granted thatÔ0For legal reasons I am required to disclose thatÔIt is elementary to show thatÔ:I donâ€™t remember why, but youâ€™ll have to trust me thatÔ.Following the logical steps, we might concludeÔ!We are all but forced to see thatÔBy the same logic,Ô,Iâ€™m not even going to bother to prove thatÔ#By Kantâ€™s Categorical imperative,Ô&Everyone and their mother can see thatÔA child could tell you thatÔ6It baffles me that you havenâ€™t already realized thatÔNotice then thatÔ'Just this once I will admit to you thatÔ&Using the proper mindset one sees thatÔ(Remember the basic laws of common sense:Ô1There is a lovely little argument that shows thatÔ-Figure 2 (not shown here) makes it clear thatÔ&Alas, would that it were not true thatÔIf Iâ€™m being honest with you,ÔSAccording to the pointy-headed theorists sitting in their Ivory Towers in academia,ÔWe will take as an axiom thatÔAccept for the moment thatÔ#These are your words, not mine, butÔA little birdie told me thatÔ"I heard through the grapevine thatÔ)In the realm of constructive mathematics,Ô,It is a theorem from classical analysis thatÔLife is too short to prove thatÔA consequence of IUT is thatÔ%As practitioners are generally aware,ÔIt is commonly understood thatÔ$As the reader is no doubt cognizant,Ô(As an exercise for the reader, show thatÔAll the cool kids know thatÔIt is not difficult to see thatÔ*Terry Tao told me in a personal email thatÔBehold,ÔVerify thatÔIn particular,Ô Moreover,Ô
Yea verilyÔBy inspection,Ô,A trivial but tedious calculation shows thatÔ$Suppose by way of contradiction thatÔBy a known theorem,Ô
HenceforthÔRecall thatÔWherefore said He unto them,ÔIt is the will of the Gods thatÔIt transpires thatÔWe findÔ,As must be obvious to the meanest intellect,Ô)It pleases the symmetry of the world thatÔAccordingly,Ô%If there be any justice in the world,ÔIt is a matter of fact thatÔIt can be shown thatÔImplicitly, thenÔ
Ipso factoÔ%Which leads us to the conclusion thatÔWhich is to sayÔThat is,ÔCThe force of deductive logic then drives one to the conclusion thatÔWhereafter we findÔZAssuming the readerâ€™s intellect approaches that of the writer, it should be obvious thatÔErgoÔWith God as my witness,ÔAs a great man once told me,Ô*One would be hard-pressed to disprove thatÔ0Even an applied mathematician would concede thatÔOne sees in a trice thatÔYou can convince yourself thatÔMama always told meÔ,I know it, you know it, everybody knows thatÔ)Even the most incompetent T.A. could see,ÔThis won't be on the test, butÔTake it from me,ÔAxiomatically,Ô
Naturally,ÔA cursory glance reveals thatÔAs luck would have it,Ô(Through the careful use of common sense,ÔBy the standard argument,Ô%I hope I donâ€™t need to explain thatÔAccording to prophecy,ÔOnly a fool would deny thatÔIt is almost obvious thatÔBy method of thinking,ÔThrough sheer force of will,ÔIntuitively,Ô*Iâ€™m sure I donâ€™t need to tell you thatÔ%You of all people should realize thatÔThe Math Gods demand thatÔThe clever student will noticeÔ'An astute reader will have noticed thatÔ*It was once revealed to me in a dream thatÔEven my grandma knows thatÔ#Unless something is horribly wrong,Ô(And now we have all we need to show thatÔ!If you use math, you can see thatÔIt holds vacuously thatÔNow check this out:Ô$Barring causality breakdown, clearlyÔPWe don't want to deprive the reader of the joy of discovering for themselves whyÔ*One of the Bernoullis probably showed thatÔSomebody once told meÔBy extrapolation,ÔCategorically,Ô:If the reader is sufficiently alert, they will notice thatÔItâ€™s hard not to prove thatÔ*The sophisticated reader will realize thatÔIn this context,Ô'It was Lebesque who first asked whetherÔAs is tradition,ÔAccording to local folklore,Ô,We hold these truths to be self-evident thatÔBy simple induction,Ô'In case you werenâ€™t paying attention,ÔIA poor student or a particularly clever dog will realize immediately thatÔFEvery student brought up in the American education system is told thatÔMost experts agree thatÔSober readers see thatÔAnd would you look at that:ÔAnd lo!ÔBy abstract nonsense,Ô/I leave the proof to the suspicious reader thatÔSWhen one stares at the equations they immediately rearrange themselves to show thatÔThis behooves you to state thatÔ ThereforeÔ1The heralds shall sing for generations hence thatÔ7If Iâ€™ve said it once Iâ€™ve said it a thousand times,Ô:Our forefathers built this country on the proposition thatÔHMy father told me, and his father before that, and his before that, thatÔ4As sure as the sun will rise again tomorrow morning,Ô7The burden of proof is on my opponents to disprove thatÔIf you ask me,Ô4I didnâ€™t think I would have to spell this out, butÔFor all we know,Ô$Promise me you wonâ€™t tell mom, butÔ;It would be a disservice to human intelligence to deny thatÔ4Proof of the following has been intentially omitted:Ô?here isnâ€™t enough space in the footnote section to prove thatÔ,Someone of your status would understand thatÔIt would stand to reason thatÔOstensibly,Ô'The hatred of 10,000 years ensures thatÔ@There isnâ€™t enough space in the footnote section to prove thatÔ,Simple deduction from peanoâ€™s axioms showsÔ(By a careful change of basis we see thatÔ%Using Conwayâ€™s notation we see thatÔThe TL;DR is thatÔ
Certainly,ÔSurelyÔ$An early theorem of Gauss shows thatÔ"An English major could deduce thatÔAnd Jesus said to his Apostles,Ô_This fact may follow obviously from a theorem, but it's not obvious which theorem you're using:ÔWord on the streets is thatÔ>Assuming an arbitrary alignment of planets, astrology tells usÔThe voices insist thatÔ4Someone whispered to me on the subway yesterday thatÔFor surely all cases,ÔIndeed,ÔLegend says thatÔAs if by design,ÔCome to think of it,Ô And as if that werenâ€™t enough,ºÐ@o Ô ÌtextÔAdd trivial statement‡