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My math is shallow at best but... 1∪2 would become just 2 with integers represented as sets in certain foundational theories, right?
by vkazanov 5y ago
My math is shallow at best but... 1∪2 would become just 2 with integers represented as sets in certain foundational theories, right?
- hansvm 5y agoYes. One common definition is equivalent to each natural to being the set containing all preceding naturals. With that view 2={0,1} and 1={0}, so their union is just 2.
- Spivak 5y agoYep! But notation depends a lot on the author to some extent. You will find people who treat 1U2 as {1}U{2} because it’s less annoying to write. It’s the same reason languages have an .add method on sets so you don’t have to write. s = s.union(set(s))
- deleted 5y ago[deleted]
- alisonkisk 5y agowho writes 1U2 instead of {1,2} ? When would {1}U{2} ever appear in ant context except for the first day of Intro to Set Theory?
- jdmichal 5y agoI assume 1 and 2 are placeholders here... Not literally meant.