Can you have more than one immediate successor?
I deliberately avoided the phrase immediate successor, because you seem to have an irrational reaction each time it is used, but yes, what I'm asking is, what is the immediate successor of [3, 5)?
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Can you have more than one immediate successor?
I deliberately avoided the phrase immediate successor, because you seem to have an irrational reaction each time it is used, but yes, what I'm asking is, what is the immediate successor of [3, 5)?
doronshadmi
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[3,5) is actually [3,... interval that followed by [5,... interval.
jfisher suggested to change [5,... by [5,5], and by doing that we can say that
[3,5) < [5,5] where [5,5] is an immediate successor of [3,5), but in order to say that, we must ignore the content (the elements) of both [3,5) and [5,5] intervals, as I wrote in http://www.internationalskeptics.com/forums/showpost.php?p=4791128&postcount=3537 .
But it is possible to say that [3,5) < [5,5] in the first place, exactly because we do not ignore the elements of [3,5) and [5,5] , so intervals of real numbers have no "<" between them without their contents.
In other words, [3,5) < [5,5] expression holds only if 5 is compared with the elements of [3,5), and as a result what is written in http://www.internationalskeptics.com/forums/showpost.php?p=4791128&postcount=3537 does not hold between intervals.
As for irrational reaction, each time you ask about an immediate successor of [3,5), this is indeed an irrational action, because [3,5) does not have an immediate successor, but you insist to repeat on this question again and again, which is an irrational re-action.
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Doron seems to be mixing up sets and set members. An interval is a set, in the case of [3,5) it is a set containing all the numbers on the real line which are greater or equal to 3 and are less than 5. This is obviously an infinite set. Within this set there is no largest member. However intervals belong to the real line, therefore the next number on the real line that succeeds this set is 5 and it is not a member of the interval. Doron thinks that because the set is infinite and contains real numbers it has no successor because he does not understand or refuses to accept that both intervals and numbers are part of the real line.
Because Doron did not go past his bizarre interpretations of simple mathematical concepts onto more advanced topics like calculus that rely on intervals for concepts as domain and others he looks at things from a very naive and uneducated standpoint. The sad thing is that he can not bring himself to admit his errors and accept other peoples authority in Math.
doronshadmi
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sympathic ,
There is a successor to [3,5) elements, and it is called 5.
But 5 is not an immediate successor of any element of [3,5) interval, as clearly seen in [3,...[5,5] .
No, you refuse to accept that "<" relation between [3,5) and [5,5] has no meaning if we ignore the relations between the elements of [3,5) and the elements of [5,5], as jsfisher tries to force, in this case.
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That's a very odd way to phrase it. Why the superfluous word, "elements"?
Nobody is saying it is.
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jsfisher supporeted it because it is correct.
That is certainly not correct.
Um, this assertion Doron…
Is yours and yours alone, so it is up to you to show … “how [X,Y)< [Y,Y] by ignoring the elements of [X,Y) and the elements of [Y,Y].”
Please let us know when you’ve got that worked out, will ya.
What do you even mean by that?
doronshadmi
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because "<" is meaningless without these elements (thet exist both in [3,5) and [5,5]
[3,5) < [5,5] is gibberish if we ignore the elements of [3,5) and [5,5].
Since this is the case, then [3,5) does not have an immediate successor.
There aren't any elements that exist in both [3, 5) and [5, 5]
doronshadmi
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http://www.internationalskeptics.com/forums/showpost.php?p=4791399&postcount=3551
Here jsfisher tries to find [X,Y) < [Y,Y], and he claims that [Y,Y] is an immediate successor of [X,Y).jsfisher said:
But thtis is utter nonsense because "<" relation between [X,Y) and [Y,Y] does not exist unless Y element of [Y,Y] interval is compared with any element of [X,Y) interval.
In this case [X,Y) does not have an immediate successor.
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doronshadmi
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Ho no, you looked on the elements and not on the intervals, noty noty boy, did you forget what jsfisher told you?
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Name one element that is in [3, 5) and [5, 5].
(I'll give you a clue, there isn't one.)
doronshadmi
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So what?
Since "<" relation between [3,5) and [5,5] cannot be found without the elements of these intervals, then [3,5) < [5,5] has a meaning only because of the comparison between [5,5] elements and [3,5) elements.
According to this comparison (that without it "<" has no meaning) [3,5) does not have an immediate successor.
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well, you referred to:
Though I suspect that you didn't mean what you said.
If that's what you want to believe...
So close. I thought you were going to get it this time.
jsfisher
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Am I alone in finding it ironic that the person who has tremendous difficulty communicating in complete thoughts is quibbling over someones use of the colloquial "if...then"?
You asked for plain English, doron, and that's what you got. Whether you accept the colloquial "if...then" as equivalent to the mathematically precise "if and only if" isn't all that important. It is what he meant. Let's move on, please.
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Yes, and I also told you how ordering between intervals and numbers was to be defined. You must have skipped over that part.
I have already shown you how the ordering relation between intervals was to be defined. All the necessary conditions are satisfied, so [X, Y) < [Y, Y]. Or do you have a counter-example to contradict that?
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jsfisher
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Ok, I must have missed this. Has doron invented yet another bit of notation?
Doron, what do you mean by this "[3,..." and "[5,..." stuff?
doronshadmi
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doronshadmi said:
By "these elements" I mean the elements of the intervals, and not particular elements that exist both in [3,5) and [5,5].
Next time try to get what you read according to the context (this is, by the way, the reason why you don't get that [3,5) does not have an immediate successor).
doronshadmi
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Interval A = [X,Y)
Interval B = [Y,Y]
We know that A and B are different and A and B have no common locations along the real-line, only if we look at their elements.
We know that A<B only by their elements, so without the elements of A and B, A<B expression cannot be found.
Since this is the case, then 'immediate successor' has a meaning here only in terms of the comparison between the elements of B interval and the elements of A interval.
By doing that, it is clearly understood that A (which is a mathematical object that does not exist independently of its elements) does not have an immediate successor.
Anyone who claims that he can compare between A and B and conclude something about the relations between A and B (by ignoring the relations between the elements of A and the elements of B) uses an illusionary game with notations, without any reasoning and notion at the basis of this illusionary game.
Jsfisher, zooterkin and The Man, plays this illusionary game with notations, without any reasoning and notion at the basis of this game, in the case of A and B intervals.
Interval B = [Y,Y]
We know that A and B are different and A and B have no common locations along the real-line, only if we look at their elements.
We know that A<B only by their elements, so without the elements of A and B, A<B expression cannot be found.
Since this is the case, then 'immediate successor' has a meaning here only in terms of the comparison between the elements of B interval and the elements of A interval.
By doing that, it is clearly understood that A (which is a mathematical object that does not exist independently of its elements) does not have an immediate successor.
Anyone who claims that he can compare between A and B and conclude something about the relations between A and B (by ignoring the relations between the elements of A and the elements of B) uses an illusionary game with notations, without any reasoning and notion at the basis of this illusionary game.
Jsfisher, zooterkin and The Man, plays this illusionary game with notations, without any reasoning and notion at the basis of this game, in the case of A and B intervals.
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