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### Ideas of Oliver,A/Smiley,T, by Text

#### [British, fl. 2006, Both at the University of Cambridge.]

 2006 What are Sets and What are they For?
 Intro p.123 14199 Cantor's sets were just collections, but Dedekind's were containers
 Intro p.124 14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality
 Intro p.125 14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set'
 1.2 p.127 14239 The empty set is usually derived from Separation, but it also seems to need Infinity
 1.2 p.129 14240 The empty set is something, not nothing!
 1.2 p.130 14241 We don't need the empty set to express non-existence, as there are other ways to do that
 1.2 p.131 14242 Maybe we can treat the empty set symbol as just meaning an empty term
 2.2 p.135 14243 The unit set may be needed to express intersections that leave a single member
 5.1 p.145 14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists
 5.1 p.146 14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics
 5.2 p.147 14247 Sets might either represent the numbers, or be the numbers, or replace the numbers