No description available.

The purpose of this composition is to develop a rigorous, axiomatic proof of the comparability of the cardinals of infinite sets.

By first looking at the orthonormal basis: Γ = {∑i 4 ibi ∈{0, 1}, finite sums} and the related orthonormal basis 5Γ = {5∑i 4i bi : bi ∈ {0, 1}, finite sums} we find several interesting relationships with the unitary matrix Uα,β arising from the operator U: Γ → 5Γ. Further, we investigate the relationships between U and the operators So : Γ → 4Γ defined by Soe4γ where eγ = e2ΠiΓ and S1: Γ → 4Γ+1 defined by S1eγ = e4γ+1. Most intriguing, we found that when taking powers of the aforementioned Uα,β matrix that although there are infinitely many 1's occurring in the entries of Uα,β only one such 1 occurs in the subsequent higher powers Ukα,β. This means that there are infinitely many γ ∈ Γ ∩ 5Γ, but only one such γ in the intersection Γ and 5kΓ, for k ≥ 2.

Thesis (Ph. D.)--University of Chicago, 1912. / "Estratto dal tomo XXXIX (1⁰ sem. 1915) dei Rendiconti del Circolo matematico di Palermo." Also available on the Internet.

Thesis (doctoral)--Friedrich-Wilhelms Universität zu Berlin, 1878. / Vita.

Thesis (Ph.D.)--University of Central Florida, 2008. / Adviser: Qiyu Sun. On t.p., "l" is small script ell and "p" is superscript. Includes bibliographical references (p. 37-38).

No description available.

Thesis (M.A.)--Trinity Evangelical Divinity School, 1987. / Abstract. Includes bibliographical references (leaves 91-96).

Habilitationsschrift--Tech. hochchule, Karlsruhe. / "Sonderabdruck aus dem 61. bande der Mathemaischen annalen."

Thesis (Ph. D.)--University of Chicago, 1931. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois."