Definition:Integer/Linguistic Note
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 its adjectival for integral (pertaining to an integer), where the g is hard (as in get): in-te-gral.
Also note the use of the word integral as an adjective, which in natural language means 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.
Also see
Sources
- 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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integral: 2.
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.2$: Elements, my dear Watson
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integral: 2.
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): $\Z$