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26 Oct 2016: Prove that every block of b. consecutive natural numbers contains two distinct numbers whose product is a multiple. ... of ab. If a, b and c are distinct natural numbers with a < b < c, must every block of c.

5 Oct 2016: 22. Except as provided in (a) and (b) below, every candidate for Part II shall send to the Chair of Examiners so as to arrive not later than the first Tuesday ... 23. Every candidate submitting a dissertation or a critical review essay under Regulation 22

10 Oct 2016: Show that for every ε > 0, there exists a finiteunion of disjoint intervals A = (a1,b1]. ... Show further that this remains true for every Borel set inR of finite Lebesgue measure.

28 Oct 2016: Prove that every block of b. consecutive natural numbers contains two distinct numbers whose product is a multiple. ... of ab. If a, b and c are distinct natural numbers with a < b < c, must every block of c.

26 Sep 2016: Next section:Section 12. ADMISSION TO DEGREES. Supplicats. 1. Every Supplicat, that is to say, every Grace for a complete degree not conferred under Statute B II 2, shall be in ... a)every titular degree shall be conferred before any complete degree is

27 Oct 2016: Show that for every ε > 0, there exists a finiteunion of disjoint intervals A = (a1,b1]. ... Show further that this remains true for every Borel set inR of finite Lebesgue measure.

8 Feb 2016: 9. Use Zorn’s Lemma to prove(i) that every partial ordering on a set can be extended to a total ordering;(ii) that, for any two sets A and B, ... Hint: consider{c L | c a b}.] Deduce that every finite distributive.

24 Oct 2016: H = {q(, ) : 2 } ,which is done as follows: First define the open balls B(, ) = {0 2 : k 0k < }, anddefine, for every 2 , the auxiliary brackets. ... 02B(,)q(x, 0). 1. so that l(x, , )  q(x, 0)  u(x, , ) holds for every x and every 0 2 B(, ). By

2 Nov 2016: Paper 4. Set texts. Paper 5. General paper. Every candidate shall offer Papers 1–5. ... d) Every candidate submitting a dissertation or a pair of essays will be required to sign a declaration that the work submitted is her or his own work, unaided

14 Oct 2016: is a limit ordinal;(c) Every limit ordinal is of the form α ω;(d) Every limit ordinal is of the form ω α. ... ix). Prove that every ordinal of the form ωα is indecomposible: γ β = ωα γ =ωα β = ωα.