The term

**ZERMELO-FRAENKEL SET THEORY** is found in the title "Ein axiomatisches
System der Mengenlehre nach Zermelo und Fraenkel," by Ernst-Jochen Thiele,
*Z.
Math. Logik Grundlagen Math.* (1955).

The term is also found in R. Montague, "Zermelo-Fraenkel set theory
is not a finite extension of Zermelo set theory," *Bull. Amer Math. Soc.*
62 (1956).

Attributions to Zermelo occur in A. Fraenkel, "Zu den Grundlagen der
Cantor-Zermeloschen Mengenlehre," *Math. Annalen* (1922) and "Über
die Zermelosche Begründung der Mengenlehre," *Jahresbericht der Deutschen
Mathematiker-Vereinigung* 30, 2nd section (1921) [James A. Landau].

**ZERO.** The Hindus called the symbol *sunya,* and the term
passed over into Arabic as *as-sifr* or *sifr* (Smith vol. 2,
page 71).

Abraham ben Meir ibn Ezra (1092-1167) used *galgal* for zero in
a description he wrote of a decimal system of numeration.

Leonardo of Pisa (1180-1250) (or Fibonacci) used the word *zephirum*
for this symbol in *Liber Abaci:* "...quod arabice zephirum appelatur."

According to Smith (vol. 2), some other old names for zero include *sipos,
tsiphron, tziphra, rota, omicron, circulus, theca, null, zeuero, ceuero,
cifra, zepiro* and *figura nihili.*

According to Cajori (1919, page 128), the word zero "is found in some fourteenth century manuscripts."

Cajori also states that the first printed treatise containing the word
zero is *De arithmetrica opusculum,* by Filippo Calandri, which was
printed in Florence in 1491. Cajori attributes this information to Eneström.
[Calandri's name is also spelled Philippus Calender and Philippus Calandrus.]

The earliest citation for zero in English in the OED2 is from 1604: "...marking the dayes with a Zero or cipher."

Older terms for this symbol in English include *aught, naught,*
and *cipher.*

The term **ZETAIC MULTIPLICATION** was coined by James Joseph Sylvester.

**ZORN's LEMMA.** Gregory Moore, in his definitive book *Zermelo's
Axiom of Choice: Its Origins, Development and Influence,* says, "By
late in 1934, Zorn's principle had found users in the United States who
dubbed it Zorn's Lemma." [Bill Dubuque] Julio González Cabillón believes
the term may have been coined by John W. Tukey.