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In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right.

Is collection a math object? or just an ordinary plain English word?

could someone please give a complete list of similar notion (something like containers)?

for example (this might be wrong), set is a math object, sequence is a math object, space is a math object, any other similar notion is NOT a math object, such as collection, list ...

JJJohn
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  • Plain old English word. Meant to give you intuition for what a set is, not used formally. (Or, when used formally, and not defined, will usually just mean “set.”) – Thomas Andrews Nov 05 '19 at 23:16
  • In my mind, this is just an informal explanation of what a set is, and (in my mind) the word "set" is actually one of the undefined terms at the base of our axiomatic systems. (There have to be some undefined terms, after all.) But I do applied math and people who study set theory carefully might have a different viewpoint. My impression is that the word "collection" is merely a synonym for the word "set". – littleO Nov 05 '19 at 23:18

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Somewhere in the middle. A collection is a set whose members are also sets. It is a convenient word because it lets you distinguish between the elements (which are sets) and the collection that binds them.

  • Thank you! Could you please give a complete list of similar notion (something like containers)? for example (this might be wrong), set is a math object, sequence is a math object, space is a math object, any other similar notion is NOT a math object, such as collection, list ... – JJJohn Nov 05 '19 at 23:51