My question is basically: true or false? I'm told this is false, but don't understand why.
- Set: A set is an unordered group of related elements which are distinct.
- Sequence: A sequence is a list of related elements which occur in a particular order.
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gattsbr
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2"Related" is debatable, and sets are not ordered. – Randall Oct 11 '17 at 17:01
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@randall typeo on ordered, was supposed to be unordered. – gattsbr Oct 11 '17 at 17:07
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What is your question exactly? Your two statements about "Set" and "Sequences" are neither true or false because "Set" is an undefined primitive concept similar to point and line in Euclidean geometry, and "Sequence" is not precise enough to be a definition. – Somos Oct 11 '17 at 17:45
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A set doesn't have a specified order. The two element set $\{1,2\}$ is the same as $\{2,1\}$.
A sequence is a list of values. You can think of a finite sequence of length $n$ as a function on the set $\{1,2,\ldots,n\}$. An infinite sequence is a function on the set of natural numbers $\mathbb{N}$.
Paul Orland
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The definition of a set is a somewhat complicated discussion as evident by Russel's paradox.The definition by Cantor (as taken from wikipedia) is "A set is a gathering together into a whole of definite, distinct objects of our perception or of our thought—which are called elements of the set." .The formality about what is a set can be explored through the axioms proposed by Ernst Zermelo and Abraham Fraenkel.
A sequence can be defined to be a function $f:\mathbb{N}\rightarrow A$ where $A$ is a set.
Pmeramv
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