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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.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