After defining ‘real’ and ‘ideal’ in relation to character or behaviour and to setting, this chapter notes that, whereas the other four Greek ‘ideal’ novelists create a realistic background, whether using personal observation or historiography, Longus draws chiefly on literary texts that themselves present a fictional world (Homer and Theocritus) or one that is semi-fictional (archaic melic poetry). ‘The Country’ explores Longus’ debt to Theocritus’ landscape, especially that of Idyll 1, advertised by his preface as several steps removed from the real world. The chapter then discusses the relation of 2.32 to Theocritus 1; of 1.17.3 to Sappho and Anacreon via Theocritus 11, complicated by the term ἀληθῶς, ‘really’; and of the apple at 3.33.4 to Sappho’s epithalamia, Ibycus, and Theocritus 28. ‘The city’ explores the literary forebears of Longus’ Megacles; ‘The sea’ looks at his ‘Tyrian’ pirates’ origins in earlier novels, especially Chariton’s; and ‘Reality’ considers how his use of Thucydides underlines his own fictionality. Overall it is the chapter’s stress on the fictionality, rather than on the poetic status, of most of Longus’ intertexts that differentiates its writer’s position from those of Richard Hunter and Maria Pia Pattoni.

Complex numbers are a critical component of the mathematics of quantum mechanics, so we provide a brief review. Topics include imaginary numbers, Euler’s formula, modulus, phase, and complex conjugate.

Altieri’s chapter defines four basic modes of thinking in Wallace Stevens’s poetry. Harmonium (1923) reconceives what poetic thinking can be—from an ideal of cogent masculine argument to the possibility of thinking against generalization. Such thinking offers allegories that fascinate without resolving. And it shifts the sensuality of poetry from an emphasis on referring to sensuous detail to a lyric sensuality that is basic to the forms of concreteness established by the workings of the medium. Second, Stevens turns in Ideas of Order (1936) from valuing the eccentric to imagining how poetic thinking can become central to ordinary life. Third, by the final poems of Transport to Summer (1947), Stevens seems to become embarrassed by his own rhetoric of the hero and major man. He becomes increasingly concerned with blending the unreal of fiction with the work of realization, a concept strikingly parallel to Paul Cézanne’s idea of how art brings force and vitality to nature. Finally, that theoretical concern for blending fictionality with realization generates in The Rock (1954) a mode of poetic thinking inseparable from a sense of self-conscious dwelling that enables us to value the artifice present in even the most elemental of experiences.

Tropes of Indigeneity both conceal and expose the tangle of land, labor, and race in the American southern context. This introduction poses Indian Removal as the underacknowledged historical thunderclap, akin to the Civil War, after which the South struggled permanently to regenerate its self-conception. In the narratives of modern and contemporary white southerners, the story of the southeastern Indian is inextricable from the white South’s story about itself - a structure built on preoccupations with loss, dispossession, sovereignty, and community. The Indian motif marks the passage from the white southern specular self to its socially constituted version, and the maintenance of that self is, in many ways, dependent on the internalization of an elaborate Indigenous fiction. What that narrative both covers over and exposes is haunting in more ways than we have realized: it is, finally, a revelatory model of not just settler colonial extermination but of the vacancies, desires, and horrors of a modernity constructed on the twin phantoms of materialism and racialism.

We construct the real numbers using equivalence classes of Cauchy sequences and show that they obey the fundamental axiom and the standard rules of arithmetic.

We show that the rationals will not support calculus. Using the intermediate value theorem, we discuss the properties required by a number system to allow us to do calculus. We state the fundamental axiom of analysis and obtain various equivalent forms of that axiom.