3 ms·
Do you know the definition of countable? A set S is countable if there is a one-to-one mapping from S to N where N is the natural numbers. Do you know that 0 is
by atwood22 4y ago
Do you know the definition of countable? A set S is countable if there is a one-to-one mapping from S to N where N is the natural numbers. Do you know that 0 is not a member of the natural numbers? We literally start counting at 1 by definition of countable.
- lupire 4y agoNope. Is the empty set countable? (Yes.) Dictionary: nat·u·ral num·bers the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well Countable: https://en.wikipedia.org/wiki/Countable_set https://en.wikipedia.org/wiki/Countable_set Set theory: https://en.wikipedia.org/wiki/Ordinal_number https://en.wikipedia.org/wiki/Ordinal_number
- atwood22 4y agoFrom your own link on countable sets: > Equivalently, a set S is countable if there exists an injective function f : S → N from S to N; it simply means that every element in S corresponds to a different element in N. Defining N is usually done via a successor set, on which case 0 makes no sense to include.
- lupire 4y agoA successor set is the set of successors of... 0 or 1, depending on what you are doing.
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- kazinator 4y agoAn empty set is countable; it has an empty mapping to the natural numbers. Its cardinality is zero.
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- lupire 4y agoAnd its ordinalitiy is also 0. Standard construction of ordinals is that each ordinal is the set of all its predecessors. (0 has no predecessors , hence 0 is the empty set.) (And so finite ordinals have the same ordinaliity as cardinality).
- pwdisswordfish9 4y agoShow me a mathematical text where ‘ordinality’ is defined.
- samatman 4y agoAre you a time traveller from the late 17th century?