Deeper than primes

[doronshadmi]

Doron,

Very early on in this current tangent you said:



But just recently you said:




These two statements are not in universal harmony. Which one would you like to retract, or will you just let the contradiction stand?

You mix up between OM and Standard Math.

My last dialog with you is only under Standard Math.

 

[doronshadmi]

So, under a very reasonable assumption for partial ordering, the interval [3, 5) precedes 5. Equivalently, [3, 5) < 5.

It does not mean that 5 is an immediate successor of anything that is related to [3,5).

5 is a successor of [3,5), as I claim

5 is not an immediate successor of [3,5), as you claim.

AGAIN: we are talking here only about Standard Math.

 

[zooterkin]

Doron, what is the next number after [3, 5)?

If it is not 5, then what do you think [3, 5) means? What are the numbers which fall in that interval?

 

[jsfisher]

You mix up between OM and Standard Math.

My last dialog with you is only under Standard Math.

Well, then, you must be using some rather interesting partial ordering for your OM case. Tell us about it. What ordering were you implicitly assuming?

 

[jsfisher]

It does not mean that 5 is an immediate successor of anything that is related to [3,5).

5 is a successor of [3,5), as I claim

It took you quite a while to finally accept this claim (and yes, the whole time under an assumption of "standard math"). If fact, just a few posts back, you proclaimed, "Again, [3,5) < 5 is gibberish."

Still, glad to have you on board, finally.

5 is not an immediate successor of [3,5), as you claim.

If 5 be not an immediate successor of [3, 5), then there'd need to be some number between [3, 5) and 5. What number could that be?

 

[doronshadmi]

Doron, what is the next number after [3, 5)?

If it is not 5, then what do you think [3, 5) means? What are the numbers which fall in that interval?

Any arbitrary value < 5, but it is not relevant to our case.

EDIT: the first row has a typo mistake, the right one is:

Any arbitrary value > 5, but it is not relevant to our case.

The relevant question here is: what is the next immediate number after [3, 5)?

 

[doronshadmi]

[3, 5) and 5. What number could that be?

jsfisher, is 5 one of the elements of [3,5) interval ( if the answer is yes than 5 is the largest element, but then we are talking about [3,5] and not about [3,5) )?

 

[zooterkin]

Any arbitrary value < 5, but it is not relevant to our case.

The relevant question here is: what is the next immediate number after [3, 5)?

Yes, that's the question I asked you. What's the answer?

 

[zooterkin]

jsfisher, is 5 one of the elements of [3,5) interval ( if the answer is yes than 5 is the largest element, but than we are talking about [3,5] and not about [3,5) ).

Oh, dear, Doron, do keep up.

No, 5 is not included in the [3, 5) interval. By definition.

 

[doronshadmi]

http://www.internationalskeptics.com/forums/showpost.php?p=4752300&postcount=3179

That's simply what the notation [X, Y) means. It refers to the finite interval starting with X, and including everything up to, but not including, Y.

http://www.internationalskeptics.com/forums/showpost.php?p=4752496&postcount=3191

The phrase, up to, is neither a real number nor an interval, so it has no part in this discussion.

There is no "up to" here.

Doron, you have such difficulty with so many simple expressions. By the way, the full expression, as was used, here, was up to but not including. To you have similar problems with between? If we describe [3, 5) as all the real numbers between 3 and 5 and including 3, will that cause you similar consternation?

Really, what's your hang-up with zooterkin's original wording?

So you contradict yourself once again, jsfisher.

Now we can see why you avoid this:

[3, 5) and 5. What number could that be?

jsfisher, is 5 one of the elements of [3,5) interval ( if the answer is yes then 5 is the largest element, but than we are talking about [3,5] and not about [3,5) )?

and also you avoid this:

Yes, really. The proof showed that the set {X : X < Y} has no largest member. There was no half-open finite interval [X, Y) anywhere in the proof.

jsfisher,

Is Y is a mamber of set {X : X < Y}?

Please answer by yes or no.

 

[jsfisher]

Any arbitrary value < 5, but it is not relevant to our case.

Let's see. I'll take 2 as my arbitrary value less than 5. So, according to Doron, 2 is the next number after [3, 5).

The relevant question here is: what is the next immediate number after [3, 5)?

Umm, that's the question zooterkin asked. (The word immediate is superfluous.)

 

[jsfisher]

So you contradict yourself once again, jsfisher.

What do you find contradictory?

On the one hand, I correctly point out that "up to" is not a number. You aren't claiming it is, are you? If so, is it bigger than 17?

On the other hand, I point out that you have difficulty understanding the phrase, "up to but not including Y".

Are you really saying those two statements are in conflict with each other?

 

[doronshadmi]

Let's see. I'll take 2 as my arbitrary value less than 5. So, according to Doron, 2 is the next number after [3, 5).

You are right, it is a typo mistake and should be > 5, so?

 

[doronshadmi]

What do you find contradictory?

On the one hand, I correctly point out that "up to" is not a number. You aren't claiming it is, are you? If so, is it bigger than 17?

On the other hand, I point out that you have difficulty understanding the phrase, "up to but not including Y".

Are you really saying those two statements are in conflict with each other?

What is this up to that not including Y, please explicitly show its value.

 

[doronshadmi]

Yes, really. The proof showed that the set {X : X < Y} has no largest member. There was no half-open finite interval [X, Y) anywhere in the proof.

jsfisher,

Is Y is a mamber of set {X : X < Y}?

Please answer by yes or no.

Still wating to your answer.

 

[zooterkin]

Try to focus, Doron.

What is the next number after [3, 5) ?

 

[doronshadmi]

What do you find contradictory?

On the one hand, I correctly point out that "up to" is not a number. You aren't claiming it is, are you? If so, is it bigger than 17?

On the other hand, I point out that you have difficulty understanding the phrase, "up to but not including Y".

Are you really saying those two statements are in conflict with each other?

Again you contradict yourself, because this "up to" case was given by zooterkin.

So you both accept and reject his "up to" phrase.

 

[doronshadmi]

Try to focus, Doron.

What is the next number after [3, 5) ?

Any arbitrary number > 5.

Now by your "up to" please show us the immediate successor afrer [3,5).

 

[zooterkin]

Any arbitrary number > 5.

Really? Why is that? Why do you miss out 5?

ETA: And why any number >5? Do you not get the meaning of 'next'?

Now by your "up to" please show us the immediate successor afrer [3,5).

5

 

[doronshadmi]

Really? Why is that? Why do you miss out 5?



5

"After" means "after any value that appears in the expression [3,5), get it (you are the one who miss out 5)?