The Sequences

[trfrm]

Ahlan wa Sahlan.

Excuse me ... .



We can seem guess the next terms in the sequence, say, $1,2,3,4,5,\cdots$ ... .

Maybe, we will say that the next terms is $6,7,8,9,10,\cdots$ ... .

But, in fact, in real line, we cannot guess the next term, because the next terms is not unique ... .

Really, the next term is undeterminated ... .

We can make various patterns by the method, called interpolation ... .


...


Let, the sequence $u_1,\dots,u_j,\dots\in\mathbb{R}$ ... .

We are asked to guess the next terms ... .

The interpolation is such that :

\[ u_n=f(a_1,\dots,a_j,n) \]

where :

$f$ is fixed function,

$a_1,\dots,a_j\in\mathbb{R}$ are unknown constant ... .

In this method, we must substitute the sequence to the pattern of interpolation ... , and ... find all $a_1,\dots,a_j$ ... .



If we are given the pattern of the sequence, however, we can guess the next terms ... .



Thank you very much for the attention ... .

Sanctus, Sanctus, Dominus Deus Sabaoth.

[trfrm]

Ahlan wa Sahlan.

phyti, which part of the word "defines" do you not understand?

If you had access to a half decent text, you could quickly find that the definition I gave is perfectly standard. As you quite obviously don't, I can only assure you that it is standard

I'm sorry ... . I forgot to add the set of real numbers ... . I have corrected my previous post ... .

Thank you for your correction ... .

I think what trfm is trying to say is that given an initial sequence, you might assume it is the beginning of the set of natural numbers (say) but actually it is an arbitrary sequence which just happens to start like that.

In other words, what is the next item in: 1, 2, 3, 4 ?

Any sane person would say, 5.

But no! The answer is "elephant"

What is the point of this thread? Is it a joke of some sort?

It's maybe ... because the elephant is an element of a set of everything ... .

Nderek langkung.