Definition of "real"

[T]he real reason he didn't come was because he was scared of flying[.]

2007, Jim Kokoris, The Rich Part of Life: A Novel, page 179

Even without hovering drones, a lurking assassin, a thumping score and a denouement, the real-life story of Edward Snowden, a rogue spy on the run, could be straight out of the cinema. But, as with Hollywood, the subplots and exotic locations may distract from the real message: America’s discomfort and its foes’ glee.

2013 June 29, “Travels and travails”, in The Economist, volume 407, number 8842, page 55

An artificial kidney these days still means a refrigerator-sized dialysis machine. Such devices mimic the way real kidneys cleanse blood and eject impurities and surplus water as urine.

2013 June 1, “A better waterworks”, in The Economist‎, volume 407, number 8838, page 5 (Technology Quarterly)

Whose perfection farr excell’d Hers in all real dignitie

1667, John Milton, “Book IX”, in Paradise Lost. […], London: […] [Samuel Simmons], […]; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873,

The dirty secret of the internet is that all this distraction and interruption is immensely profitable. Web companies like to boast about […], or offering services that let you […] "share the things you love with the world" and so on. But the real way to build a successful online business is to be better than your rivals at undermining people's control of their own attention.

2013 June 21, Oliver Burkeman, “The tao of tech”, in The Guardian Weekly, volume 189, number 2, page 27

I waked, and found / Before mine eyes all real, as the dream / Had lively shadowed.

1667, John Milton, “Book VII”, in Paradise Lost. […], London: […] [Samuel Simmons], […]; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873,

Many are perfect in men's humours that are not greatly capable of the real part of business.

1625, Francis [Bacon], “Of Cunning”, in The Essayes […], 3rd edition, London: […] Iohn Haviland for Hanna Barret

There have been several classical constructions of the reals that avoid these problems, the most famous ones being Dedekind Cuts and Cauchy Sequences, named respectively for the mathematicians Richard Dedekind (1831 - 1916) and Augustine Cauchy (1789 - 1857). We will not discuss these constructions here, but will use a more modern one developed by Gabriel Stolzenberg, based on "interval arithmetic."

2007, Mark Bridges, REAL ANALYSIS: A Constructive Approach, Hoboken, New Jersey: John Wiley & Sons, page 11

Scotists, Thomists, Reals, Nominals

1624, Democritus Junior [pseudonym; Robert Burton], The Anatomy of Melancholy: […], 2nd edition, Oxford, Oxfordshire: Printed by John Lichfield and James Short, for Henry Cripps

Within weeks of this bombshell, an aide to the brother of the chairman of the PT, José Genoino, was arrested boarding a flight with 200,000 reais in a suitcase and $100,000 in his underpants.

2011, Perry Anderson, “Lula's Brazil”, in London Review of Books, 33.VII