Deeper than primes

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doronshadmi said:
I agree with you (it can't be), so you have to ask jsfisher about it (he is the one that claims that there is no connection between set {X:X<Y} and [X,Y) ).
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To avoid further ambiguity, where does he do that?

ETA: What connection do you think there is? Can you remember what point you were trying to make when you started this particular digression?

It means that Y is not a member to the interval [X,Y).
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Yes, but not only that. It means that Y is the immediate successor to [X, Y).
 
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doronshadmi said:
I agree with you (it can't be), so you have to ask jsfisher about it (he is the one that claims that there is no connection between set {X:X<Y} and [X,Y) ).
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No, I claimed I didn't reference any [X, Y) interval in the proof. I also claimed that X never appeared as a free variable in the proof.

I also also claimed that you keep misrepresenting {X : X < Y} as [X, Y).

It means that Y is not a member to the interval [X,Y).
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It means considerably more than that.
 
doronshadmi said:
No, you are unclear of how that would works, so please direct us to some professional source that clearly talks about Y as am immediate successor of [X,Y) (as you claim).
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Well, how about we start with your claim, since it did come first, after all. The current discussion tangent arose from your insistence the interval [X, Y) guaranteed Y must have an immediate predecessor.

So, please direct us to some professional source that clearly talks about Y having an immediate predecessor in [X,Y) (as you claim).
 
jsfisher said:
Well, how about we start with your claim, since it did come first, after all. The current discussion tangent arose from your insistence the interval [X, Y) guaranteed Y must have an immediate predecessor.

So, please direct us to some professional source that clearly talks about Y having an immediate predecessor in [X,Y) (as you claim).
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You will not find any professional source (based on Standard Math) that clearly talks about Y having an immediate predecessor in [X,Y).

Since you are using only Standard Math and claim that Y is an immediate successor of [X,Y) (and now we are talking only on Standard Math framework), then please provide this Standard Math source.

Also this time please do not avoid the question in http://www.internationalskeptics.com/forums/showpost.php?p=4786190&postcount=3400, as you did in your http://www.internationalskeptics.com/forums/showpost.php?p=4786549&postcount=3406 reply.
 
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doronshadmi said:
You will not find any professional source (based on Standard Math) that clearly talks about Y having an immediate predecessor in [X,Y).
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Is anyone claiming you will?

Since you are using only Standard Math and claim that Y is an immediate of [X,Y), then please provide this Standard Math source.
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If you mean 'immediate successor', then that's what the notation means. Why don't you get this? http://en.wikipedia.org/wiki/Interval_(mathematics)
 
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Doroshani appears to be disputing the meaning of 'immediate successor'. Perhaps he might explain what he means by it if not Y of [X, Y).
 
jsfisher said:
I separately alleged the set { X : X < Y } for some Y has no largest element. You seem hung up on this one, too, so I will support the claim.
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Here jsfisher defines set A such that any member of set A < some Y, and he wants to show that A has no largest member.

By this construction it is clear that Y is not a member of A, otherwise Y is the largest member of A, and we cannot prove that A does not have the largest member.

Since Y must not be a member of A and A's members are non-finite R members that each one of them < Y, then A members are some non-finite R elements that exist in the clopen interval [W,Y), where W is the smallest member of A set.

jsfisher said:
I will use a simple proof by contradiction. As with all such proofs, it begins with an assumption then proceeds to construct a contradiction, thereby showing the assumption to be false.

Assume the set {X : X<Y} does have a largest element, Z.

For Z to be an element of the set, Z < Y.
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Now jsfisher provides the assumption, which claims that the non-finite set A that is based on the clopen interval [W,Y), has the largest member called Z, which is a member of A set (and an element of [W,Y) interval).
jsfisher said:
Let h be any element of the interval (Z,Y).
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Here we clearly see the open side ",Y)" of the clopen interval [W,Y), that jsfisher claims that this clopen interval is not a part of his proof. But the fact is that Z is a member of A and < Y, exactly because we deal here with the clopen interval [W,Y).
jsfisher said:
By the construction of h, Z < h < Y.
Since h < Y, h is an element of the set {X : X<Y}.
Since Z < h, the assumption Z was the largest element of the set has been contradicted.

Therefore, the set {X : X<Y} does not have a largest element.
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We can clearly see that since A has no largest member, then jsfisher claim ( see http://www.internationalskeptics.com/forums/showpost.php?p=4721582&postcount=2864 ) that Y is the immediate successor of A set ( that its members are the elements of the clopen interval [W,Y) ), is a false claim.
 
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doronshadmi said:
We can clearly see that since A has no largest member, then jsfisher claim ( see http://www.internationalskeptics.com/forums/showpost.php?p=4721582&postcount=2864 ) that Y is the immediate successor of A set ( that its members are the elements of the clopen interval [W,Y) ), is a false claim.
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Obviously some previously unknown use of the word 'clearly'.

Let's try a concrete example. Take X=3, Y=5, so [3, 5).

Any number >=3 and <5 is in the interval. Pick any number you like, and it's possible to say exactly whether it is in the set or not. 5 is the immediate successor of the interval.
 
zooterkin said:
Obviously some previously unknown use of the word 'clearly'.

Let's try a concrete example. Take X=3, Y=5, so [3, 5).

Any number >=3 and <5 is in the interval. Pick any number you like, and it's possible to say exactly whether it is in the set or not. 5 is the immediate successor of the interval.
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No, 5 is a successor of any arbitrary element of [3,5) (which is trivial) and it is not an immediate successor of any arbitrary element of [3,5) , as jsfisher claims, because given any arbitrary element Z in [3,5) there is h in [3,5) such that Z<h<5, so 5 is not an immediate successor of Z.
 
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doronshadmi said:
No, 5 is a successor of any arbitrary element of [3,5) (which is trivial) and it is not an immediate successor of any arbitrary element of [3,5) , as jsfisher claims, because given any arbitrary element Z in [3,5) there is h in [3,5) such that Z<h<5, so 5 is not an immediate successor of Z.
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What?

5 is the immediate successor of the interval, not of any arbitrary element in the interval.
 
zooterkin said:
What?

5 is the immediate successor of the interval, not of any arbitrary element in the interval.
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Again:

If jsfisher claims (in this case) that 5 is an immediate successor of the open interval [3,5) (by avoiding any particular element of it) he actually takes anything that starts with 3 and < 5 as a one mathematical object, exactly as the non-finite sequence 0.9+0.09+0.009+ … is considered as a one mathematical object (=1).

But in the case of a one mathematical object that is based on 0.9+0.09+0.009+ …=1 we really deal (according to Standard Math) with the non-finite (0.9+0.09+0.009+ … =1 and <1 does not hold), where in the case of [3,5) we do not deal with the non-finite, and this is exactly the reason of why "<5" expression holds (in the first place) in 3<5, Z<5 or Z<h<5 cases.

zooterkin said:
5 is the immediate successor of the interval ...
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Immediate successor means that there is no object between 5 and any given member of [3,5) interval, if "<5" is used.

Since "<5" is used and h is between 5 and any given member of [3,5) interval, then 5 is not the immediate successor of [3,5) interval.
 
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doronshadmi said:
If jsfisher claims (in this case) that 5 is an immediate successor of the open interval [3,5)
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It's not a claim, that's what [3,5) means.
(by avoiding any particular element of it) he actually takes anything that starts with 3 and < 5 as a one mathematical object, exactly as the non-finite sequence 0.9+0.09+0.009+ … is considered as a one mathematical object (=1).
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1) Why do you keep saying 'a one mathematical object'? It's not English.
2) Why are you trying to draw some equivalence between an interval and a single number?
3) Why do you keep using 'non-finite'?
Immediate successor means that there is no object between 5 and any given member of [3,5) interval, if "<5" is used.
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Not so. The interval starts at 3 and includes all the numbers up to, but not including, 5. There will always be at least one value between any given number in the interval and 5.
Since "<5" is used and h is between 5 and any given member of [3,5) interval, then 5 is not the immediate successor of [3,5) interval.
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Quite right, 5 is not the immediate successor of 'h'. However, it is the immediate successor of [3,5) because that's what [3,5) means.
 
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