# Thread: The Sequences

1. Excuse me ... .

We can seem guess the next terms in the sequence, say, ... .

Maybe, we will say that the next terms is ... .

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 ... .

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

The interpolation is such that : where : is fixed function, are unknown constant ... .

In this method, we must substitute the sequence to the pattern of interpolation ... , and ... find all ... .

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

Thank you very much for the attention ... .   2.

3. I am sorry to appear rude, but this is a terrible muddle.

Let's see.....,.,We assume the existence of the natural numbers , also known as the "counting numbers"

We assume 2 properties of this set

1. There exists a least element in which by convention one calls as 1

2. We assume that every has a successor element denoted by Then, given an arbitrary set , then the mapping defines a sequence in such that is, by convention written as for all Thus the sequence .

So given , say, how hard is it to guess the next element in the sequence?

Your problem stems from the fact that you fail to distinguish between domains and codomains  4. Originally Posted by Guitarist I am sorry to appear rude, but this is a terrible muddle.

Let's see.....,.,We assume the existence of the natural numbers , also known as the "counting numbers"

We assume 2 properties of this set

1. There exists a least element in which by convention one calls as 1

2. We assume that every has a successor element denoted by Then, given an arbitrary set , then the mapping defines a sequence in such that is, by convention written as for all Thus the sequence .

So given , say, how hard is it to guess the next element in the sequence?

Your problem stems from the fact that you fail to distinguish between domains and codomains
You are not rude, but presumptuous.
The poster didn't specify the set of natural numbers. You are assuming this. The integers 1,2,3,4,5 could be a random sequence, or one from an unlimited number of algorithms.
Unless you specify the algorithm/function used to select the sample, you cannot know what the next element will be.  5. 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  6. 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?  7. Originally Posted by Guitarist 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 ... . Originally Posted by Strange 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 elemen of a set of everything ... .  8. Originally Posted by trfrm It's maybe ... because the elephant is an element of a set of everything ... .
Yeah well, you need to be very careful here.

Let me explain, using as little mathematical notation as clarity permits, as it appears you not mathematically sophisticated (this is not a criticism BTW, simply an observation).

So suppose there exists a set of everything, which I can call . Then the set of elephants is obviously a subset of . And so is the set of "things" that are definitely NOT elephants. The set of elephants is a subset of mammals, also a subset of , and so is the set of "non-elephant" mammals.

Both these sets are subsets of a subset of which we may call "life forms", and so is the set of "non-life forms".

Continuing in this fashion, assuming you haven't already lost the will to live, we arrive at the conclusion that the set of everything contains as a subset all those "things" that are not members of .

This a contradiction known as Russell's Paradox  Bookmarks
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