Definition·D085
n-tuples from a set
The finite sequences from a set whose length is exactly n.
For a set
and
:
the set of
-tuples from
.
In words
The set of n-tuples from A is the finite sequences from A whose length is exactly n.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
A special case of Seq(A), carved out by Separation.
always, a single-point set (the empty sequence is the only sequence of length
). Used to interpret function and relation symbols of a fixed arity in a language's structures.