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