All sequence riddles are wrong .why?

[lurflurf]

No because sequences are by definition subsets of N.

Those are natual number sequences

There are real sequences like
3,3.1,3.14,3.1415,3.1415926,3.141592653...
rational seqences
.1,.11,.111,.1111,.11111,...

A sequence is a mapping of the natural numbers to an arbitrary set
or if one prefers
we can define a seed and a map f:S->S
ie
seed=a0
a1=f(a0)
sucsessor(an)=an+1
f^n(seed)=an

 

[lurflurf]

All this said there is some value in trying to choose a best in some sense sucsession function given a run of a sequence
thhe trouble is knowing which sense our some sense should be

 

[lurflurf]

A sequence is a mapping of the natural numbers to an arbitrary set
or if one prefers
we can define a seed and a map f:S->S

Oops not general enough
we will just go with
f:N->S
S an arbitrary set
so maybe we have

1,2,3,4,5,...,88,89,pickles

 

[Diffy]

A sequence is a mapping of the natural numbers to an arbitrary set
n

I may just be playing devil's advocate, but who says sequences have to be infinite?

1, 3, 4, 6, 8 ...

what comes next? perhaps the answer is undefined, or nothing.

 

[lurflurf]

good point there are I speak of one popular sequence there are also
finite sequences
double sequences
sequences over other index sets like
Moore-Smith sequences

many times the tradition sequence structure can be used
such as
11/8,9/7,7/6,5/5,3/4,1/3,-1/2,-3/1,-5/0,-7/-1
we could interpet formally, or if it is to be interpeted as division well could mark problems as "undefind" which we could ad to the domain

for finite sets we could repeat the final entry of append a sybmol
1,2,3,4,5
could be
1,2,3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,...
0r
1,2,3,4,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
or
1,2,3,4,5,done,done,done,done,done,...