I have this problem i am trying to work on but am confused about this definition
integer k >=1, show that the set of all k-tuples {(i1, i2, · · · , ik) where ij belongs to N, 1<=j<=k}..
For example can someone just show me what tuples of size 2 would look like please?
Given , the set in question is . It says that indices are between 1 and ; nothing is said about the range of except that they are natural numbers.
k-tuples are just (ordered) sequences of length k. Nothing tricky here. The only reason they are called sequences and not sets is that the order and multiplicity (the number of times an element occurs in a sequence) of elements in a sequence matter: if you swap two unequal elements or remove one of two equal elements, you get a different sequence, which is not true for sets. See also Wikipedia.