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 |