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1.7 Real Vocab
| Term | Definition |
|---|---|
| Equivalent Sets | Two sets A and B are said to be equivalent (or have the same cardinality), denoted A~B, if there exists a one-to-one function of A onto B. |
| Finite | For each positive integer n, let ℕn = {1, 2, ..., n}. If A is a set we say A is finite if A~ℕn for some n, or if A = ∅ |
| Infinite | A is infinite if A is not finite |
| Countable (denumerable) | A is countable if A~ℕ |
| Uncountable | A is uncountable if A is neither finite nor countable |
| At most countable | A is at most countable if A is finite or countable |
| Sequence | If A is a set, by a sequence in A we mean a function f from ℕ into A. For each n ∈ ℕ , let xn = f(n). Then xn is called the nth term of the sequence f. We denote sequences by {xn} from n=1 to infinity |
| Indexed family of subsets | Let A and X be nonempty sets. An indexed family of subsets of X with index set A is a A is a function from A into P(X) {Ea} a ∈ A |
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Mollygsmithh
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