Linguistic Note on Integer
The word integer is pronounced with the stress on the first syllable, and the g is soft (i.e. sounds like j): in-te-jer.
This is inconsistent with the pronunciation of the related term integral where the g is hard (as in get): in-te-gral.
Also note the use of the word integral as an adjective, meaning necessary or inherent, usually encountered in rhetoric. For further confusion, this is pronounced in-teg-ral, the stress being on the second syllable.
The symbol $\Z$ is for Zahlen, which is German for whole numbers, with overtones of unbroken.
This is reflected in English in the word integrity, which means wholeness in the sense of unbrokenness. The word also has a similarly applicable definition in the context of moral philosophy.
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: The Notation and Terminology of Set Theory: $\S 1$
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $2$: Integers and natural numbers: $\S 2.1$: The integers
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.2$: Elements, my dear Watson