So what if you had [1, 5] and (6, 10]? What would be the difference then? Maybe 0.99999...., with an infinite number of nines or something?
Seems the more specific I try to get with this the more my eyes cross
Yea, I've heard that there have been mathematicians who literally went nuts over stuff like this. Some people take their numbers too seriously
Uhm...ionno.
Wouldn't (0.999...) only be considered the same as (1) if you rounded it? I mean, sure, they are virtually allllllmost the same but I think its just that our notation system doesn't have a means of writing out the answer to stuff like ((1) - (0.999...)). This continuum stuff is really freaky *_*
Okey, good. I got some other questions
If you're upset about jsfisher's use of the plural: I agree wholeheartedly with his post. That makes it plural. I guess there are a lot more posters in this thread who agree with it.
We shell know at the moment he will write his first post.
. Recently I have develop an algorithm to calculate the number of distinctions of a number Or . The sequences started with 1,2,3,9,24,76,236,785, …( we calculate it until or(12))
And it goes on like this?
That's clear. But why do you ignore it?
So what does this "distinction" mean? The partition part is clear, function g is clear, but then you define D and Or, mutually recursive, and I have no idea what is going on here. I can calculate it all right, but what is the meaning behind these formulae? What does it signify. The above two lines don't really help me.
Thank you jsfisher !
I think that the main new idea for us here is to begin with is to observe a number n as a superposition of its partitions Pr
I made some correction following your remarks – thank you !
Do you have some more remarks?
Moshe Klein
Sorry for my English..
to the forum.
Okey, good. I got some other questions
Once, I asked my HS geometry teacher "If there are two rods that are infinitely long but one is 2 ft wide and the other only 1ft wide, is one bigger than the other?" He just kinda shook his head and said that was a question for philosophers >_<
Got a more satisfactory answer for me?
function.=1.=2. value is based on the following:Let us show my calculations that stand at the basis of Moshe's Or
1) Organic Number n is the all possible states of Distinction between n elements, where order has no significance.
2) In n=1 there is only one state of distinction, so Or
3) In n=2 the are two possible states of distinction, for example: •• and ••, so Or
4) From n=3 and further Or
a) First we take the partitions of n which are not of the form n+0, for example:
If n=3 we take 1+1+1, 2+1 and ignore 3+0
If n=4 we take 1+1+1+1, 2+1+1, 2+2, 3+1 and ignore 4+0
Ect. …
b) Now we are using the recursion function D on each partition of some n (the case n+0 is ignored), for example let us take n=3:
The calculated partitions of n=3 are D(1+1+1) and D(2+1) (D(3+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).
Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1)=2
So, Or(3)=D(1+1+1)+D(2+1)=3
The calculated partitions of n=4 are D(1+1+1+1), D(2+1+1), D(2+2) and D(3+1) (D(4+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).
Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1+1)=2
The case of any partition of the form (2,2,2,…) is calculated by D as the result of the amount of the repetitions of number 2 in the partition+1, for example:
D(2+2)=3, D(2+2+2)=4, D(2+2+2+2)=5 , etc. …
So in the case of n=4 the result of the recursion D on partition (2+2) is D(2+2)=3
Since 3 has only three cases of distinction, then D(3+1)=3
So, Or(3)=D(1+1+1)+D(2+1+1)+ D(2+2)+ D(3+1)=9
5) The further calculations of D that are not based on (2+2+…) partitions, are as follows:
a) If the elements of a given partition are distinct - for example partition (3+2) of n=5 – then the value of D(3+2) = Or(3)*Or(2)=6. In general D(n1,n2,n3,…)= Or(n1)*Or(n2)*Or(n3)* …
b) If the elements of a given partition are non-distinct - for example partition (3+3) of n=6 – then the value of D(3+3) = (Or(3)+(Or(3)-1)+Or(3)-2)+(Or(2)+Or(2)-1)+(Or(1)) = (3+2+1)+(2+1)+(1)=10. D(3+3+3) = ((3+2+1)+(2+1)+(1)) + ((2+1)+(1)) + ((1)) = 15 (partition (3+3+3) belongs to n=6)
6) The partition is a mixing of distinct and non-distinct elements (for example partition (3,3,2) of n=8) the we first calculate 3 according (b) and then multiply the result of (b) with the result of Or(2).
In the case of partition (3,3,2,2) of n=10, we first calculate 3 and 2 cases according to (b) and then we mutably the results.
I hope that I did not make mistakes here, but it there are mistakes, I'll fix them later.
function.=1.=2. value is based on the following:
Well I get the idea, as Apathia explained it, and, as I already said, it seems to fit with what's in the document, but I would like to see a worked example of a real-world situation to which this language has been applied to analyse and/or resolve a mathematical/scientific problem with its moral and ethical implications.
