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In German mathematics, the expression ‘Zu zeigen’ exists, which translates to ‘to show’. It is used at the beginning of proofs (or the answers to exercises) to state what exactly will be shown in the following paragraph(s), for example:

Z.z.: Für jedes a,b reell existiert ein c sodass a+b=c.

‘Zu zeigen’ is often abbreviated as ‘Z.z.’, even Latex code exists to implement a nice ‘zu zeigen’ in one’s proofs.

My question is whether a similar short statement, ideally with an accompanying abbreviation, exists in English.

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In principle, QED that which must be proven should fit the bill, but in practice this invariably appears after the proof, not before. Writers generally just use something along the lines of we will show that... before the proof. –  FumbleFingers Oct 28 '12 at 17:22
To Prove: For every real a,b there exists a c such that a+b=c. Or simply Theorem:, abbr Thm:. –  John Lawler Oct 28 '12 at 17:24
I'd say To be proven: –  Mr Lister Oct 28 '12 at 21:02
@FumbleFingers QED is quod erat demonstrandum - literally, "which was to be demonstrated", so it belongs at the end. At the top you'd put simply demonstrandum, "the thing to be demonstrated". –  StoneyB Oct 29 '12 at 3:07
@JorgeCampos I usually use $\mathrm{Z\kern-.3em\raise-0.5ex\hbox{Z}}$, stolen somewhere from the web, but I cannot find the original source at the moment. –  Claudius Nov 7 '12 at 19:36

1 Answer 1

I have seen To show: used far more frequently than To prove:, at least in textbook proof exercises. I haven't seen either of them abbreviated, except for leaving out the colon. (Leaving out the colon is a minor mistake.) Occasionally the inference symbol, ⊢, is used by itself to introduce items to be proved. More properly it is a relational operator, such that x ⊢ y means y is derivable from x.

In mathematical papers or texts, rather than in exercises, forms like “We will show that...” or “We show that...” or “We prove...” or “We have...” etc. appear, particularly in text leading up to statement and proof of theorems or lemmas. For simple items, Lemma: by itself or with a number (eg, Lemma 3.5: is a common form, and 3.7. Lemma: less common) introduces something to be proven, without more needing to be said, and the proof follows after Proof:.

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