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.
2026-05-16 02:35:45.1778898945
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Sets and Sequences
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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.
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 $\mathbb{N}$.