@optumissed
You keep skipping the question: what is your argument against Cantor?
@tygxc you keep skiping this question: Because a supercomputer calculating x number of moves fail to find a win, how does that assue that a maskine calculating x +1 moves would fail to find a win?
tygxc's living in a fantasy and this possibility cannot exist to him. this has been pointed out to him for YEARS and he continues to ignore it.
@optumissed
You keep skipping the question: what is your argument against Cantor?
@tygxc you keep skiping this question: Because a supercomputer calculating x number of moves fail to find a win, how does that assue that a maskine calculating x +1 moves would fail to find a win?
tygxc's living in a fantasy and this possibility cannot exist to him. this has been pointed out to him for YEARS and he continues to ignore it.
His argument against Cantor was that Cantor introduced numbers which were finite and not finite at the same time. Which he didn't.
His argument against Cantor was that Cantor introduced numbers which were finite and not finite at the same time. Which he dididn't.
Yes, ive seen 2 things.
1) that a infinite list of finite numbers make it so that some of the numbers ar both finite and infinite at the same time
2) that since the list is infinite it can not be messured.
Regarding two infinite lists, one being larger, that is impossible for the reason that infinity is not finite. If it is not finite, then it cannot be quantified and therefore one list cannot be shown to be larger. Again, it might be ambiguous. It can conceivably be both larger and not larger, depending on perspective, just as 0/0 is both 0 and 1, depending on perspective, although 0 is literally correct and 1 consists of a kind of accomodation of rational thought into an irrational process, to keep mathematicians happy that there isn't a disjunct in the series of fractions tending towards zero in the progression, - infinity to + infinity. (Or -1 to 1)
If you can understand that, I'll talk to you some more. If you can't understand it, it would be hard work.
Now I atleast understand your position, but it seams to come from a failure to understand set theory and formal logic, but you dont have to quatefy something to show that its larger / smaler, you can use pure logic.
Imagne two lists. One containing all Mothers, the other containing all children. Without a single number we can say the first list is biger then the second. So your notion that something has to be quantified ro be able to say if its bigger or smaler is false
That logic doesn't work with an infinite number of mothers (nor with a finite number unless you know there's a mother with more than one child). If you temporarily define a mother as an even natural number starting with 0 and the children of a mother as the mother herself and the mother +1, then there's a 1-1 correspondence between the mothers/2 and the children, so both lists are the same size.
@optumissed
You keep skipping the question: what is your argument against Cantor?
@tygxc you keep skiping this question: Because a supercomputer calculating x number of moves fail to find a win, how does that assue that a maskine calculating x +1 moves would fail to find a win?
tygxc's living in a fantasy and this possibility cannot exist to him. this has been pointed out to him for YEARS and he continues to ignore it.
His argument against Cantor was that Cantor introduced numbers which were finite and not finite at the same time. Which he didn't.
Most likely he's confused himself by reading something about Dedekind finite and infinite numbers. He wouldn't have been able to understand it and decided he'd take it to mean Cantor introduced numbers which were finite and not finite at the same time.
His argument against Cantor was that Cantor introduced numbers which were finite and not finite at the same time. Which he dididn't.
Yes, ive seen 2 things.
1) that a infinite list of finite numbers make it so that some of the numbers ar both finite and infinite at the same time
2) that since the list is infinite it can not be messured.
My God. It appears that reading @Optimissed's posts can be hazardous to your mental health. We should insist on a Government health warning with each.
Yes, the first of those quoted claims is nonsensical and the second is wrong. Neither is any reflection on the work by Cantor, which remains valid today.
It's instructive to realize that while a lot of mathematics had been done by the 19th century, there was no real attention to the foundations. Mathematicians didn't really think in terms of axioms and formal systems. There was no formal construction of the real numbers, they were just assumed to exist with familiar properties.
Cantor had the insight to study very abstract objects, general sets, and he discovered some surprising and useful things about their properties (especially regarding their cardinalities - sizes). Because of the state of mathematics at that time (without the formal foundations) this was viewed with some suspicion and not accepted by everyone - apparently Kronecker (famous to students because of the Kronecker Delta 
) didn't like these developments.
Another mathematician at the time, Dedekind, found a way of formally constructing the real numbers using sets, using a similar viewpoint to Cantor.
Then there was a crisis. All this early work assumed that sets required no formal construction - they were just arbitrary collections of things. If you could define a property that could be true or false, the set of objects with that property was a meaningful thing that you could work with.
Bertrand Russell showed this was wrong a bit later (1901 perhaps?) by showing that defining sets in a perfectly plausible way led to a contradiction. And this led to the need for an axiomatic set theory. I think the second one created was the Zermelo-Fraenkel set theory which has been used as the usual foundation of all mathematics since.
The point of this story is that to do mathematics and avoid inconsistencies, you need to be very precise about axioms and definitions. Assuming intuitive notions without axiomatisation may lead to disaster.
The great thing about formal systems is that all results in them are mechanisable - the axioms and the reasoning can be manipulated precisely in a computer so there is no ambiguity. The room for interpretation is in the meaning - a set of axioms and theorems is a formal thing without a specific relationship to any "real" objects. In fact you can have different "models" corresponding to the same formal system. But generally speaking it is very clear what the meaning of the objects defined with a set of axioms is. The natural numbers, the real numbers, vector spaces and so on.
@optumissed
You keep skipping the question: what is your argument against Cantor?
@tygxc you keep skiping this question: Because a supercomputer calculating x number of moves fail to find a win, how does that assue that a maskine calculating x +1 moves would fail to find a win?
tygxc's living in a fantasy and this possibility cannot exist to him. this has been pointed out to him for YEARS and he continues to ignore it.
His argument against Cantor was that Cantor introduced numbers which were finite and not finite at the same time. Which he didn't.
I think anyone would be forgiven for assuming that you have the reading skills of a five year old but I know better. You're a pathological liar, aren't you?
Why do you have such a bad character, Elroch? What went wrong with you to make you a person who seeks refuge with profiles like player and Dio because pretty much most people despise you?
I think anyone would be forgiven for assuming that you have the reading skills of a five year old but I know better. You're a pathological liar, aren't you?
Why do you have such a bad character, Elroch? What went wrong with you to make you a person who seeks refuge with profiles like player and Dio because pretty much most people despise you?
Reality check time.
Although your reading skills are poor and I said no such thing, come to think of it, I could support the argument that the transfinite numbers are finite and infinite at the same time, since they are finite in that they represent a definite ratio, which isn't between simple numbers, so that pie is the ratio of circumference to diameter. That's the finite aspect and it's finite because it's a fixed ration that may be observed in real life: and yet it's certain that there's an infinite aspect, since numerically expressed, pie is an infinite and irrational series of numbers. Therefore pie is definitely infinite and finite at the same time.
However, that wasn't my argument and you are a complete berk for deliberately lying.
Regarding two infinite lists, one being larger, that is impossible for the reason that infinity is not finite. If it is not finite, then it cannot be quantified and therefore one list cannot be shown to be larger. Again, it might be ambiguous. It can conceivably be both larger and not larger, depending on perspective, just as 0/0 is both 0 and 1, depending on perspective, although 0 is literally correct and 1 consists of a kind of accomodation of rational thought into an irrational process, to keep mathematicians happy that there isn't a disjunct in the series of fractions tending towards zero in the progression, - infinity to + infinity. (Or -1 to 1)
If you can understand that, I'll talk to you some more. If you can't understand it, it would be hard work.
Now I atleast understand your position, but it seams to come from a failure to understand set theory and formal logic, but you dont have to quatefy something to show that its larger / smaler, you can use pure logic.
Imagne two lists. One containing all Mothers, the other containing all children. Without a single number we can say the first list is biger then the second. So your notion that something has to be quantified ro be able to say if its bigger or smaler is false
That logic doesn't work with an infinite number of mothers (nor with a finite number unless you know there's a mother with more than one child). If you temporarily define a mother as an even natural number starting with 0 and the children of a mother as the mother herself and the mother +1, then there's a 1-1 correspondence between the mothers/2 and the children, so both lists are the same size.
1. Seems to be the wrong way round. If N(M) is the number of mothers and N(C) is the number of children, N(M) <= N(C) The definition of a mother is that they have at least one child (which cannot be shared with another mother. I am assuming we are being biological here. Same sex parents would make this reasoning invalid).
2. The inequality is not strict even for finite examples. While for every mother, there must be a child (which has a unique) mother, there is no logical necessity for any to have two. Note that I am assuming it is possible to have a mother that is not a child, which might involve some major- bio-engineering
3. The same inequality would apply, with similar assumptions, if there were any infinite number of children.
4. When there are an infinite number of children, if each mother can only have a finite number of children the cardinalities are equal - N(M) = N(C). In the rather artificial case where a mother could have an infinite number of children, the inequality reappears. For it to be a strict inequality, you would need at least one mother having an infinite number of children of cardinality greater than the number of mothers. This is getting increasingly far from practical (it did that as soon as there were infinite numbers of any type)
A related fact about cardinal numbers is that if A and B are two cardinal numbers and at least one of them is infinite, then A * B = max(A, B).
I think anyone would be forgiven for assuming that you have the reading skills of a five year old but I know better. You're a pathological liar, aren't you?
Why do you have such a bad character, Elroch? What went wrong with you to make you a person who seeks refuge with profiles like player and Dio because pretty much most people despise you?
Reality check time.
Yes indeed, you are strongly disliked, even more than E, for similar reasons. A bully, a nasty piece of work, completely dishonest and so forth. And of similar intellect.
Don't worry, I am sure @DiogenesDue is as completely unconcerned by you disliking him as I am.
Regarding two infinite lists, one being larger, that is impossible for the reason that infinity is not finite. If it is not finite, then it cannot be quantified and therefore one list cannot be shown to be larger. Again, it might be ambiguous. It can conceivably be both larger and not larger, depending on perspective, just as 0/0 is both 0 and 1, depending on perspective, although 0 is literally correct and 1 consists of a kind of accomodation of rational thought into an irrational process, to keep mathematicians happy that there isn't a disjunct in the series of fractions tending towards zero in the progression, - infinity to + infinity. (Or -1 to 1)
If you can understand that, I'll talk to you some more. If you can't understand it, it would be hard work.
Now I atleast understand your position, but it seams to come from a failure to understand set theory and formal logic, but you dont have to quatefy something to show that its larger / smaler, you can use pure logic.
Imagne two lists. One containing all Mothers, the other containing all children. Without a single number we can say the first list is biger then the second. So your notion that something has to be quantified ro be able to say if its bigger or smaler is false
That logic doesn't work with an infinite number of mothers (nor with a finite number unless you know there's a mother with more than one child). If you temporarily define a mother as an even natural number starting with 0 and the children of a mother as the mother herself and the mother +1, then there's a 1-1 correspondence between the mothers/2 and the children, so both lists are the same size.
1. Seems to be the wrong way round. If N(M) is the number of mothers and N(C) is the number of children, N(M) <= N(C) The definition of a mother is that they have at least one child (which cannot be shared with another mother. I am assuming we are being biological here. Same sex parents would make this reasoning invalid).
2. The inequality is not strict even for finite examples. While for every mother, there must be a child (which has a unique) mother, there is no logical necessity for any to have two. Note that I am assuming it is possible to have a mother that is not a child, which might involve some major- bio-engineering
3. The same inequality would apply, with similar assumptions, if there were any infinite number of children.
4. When there are an infinite number of children, if each mother can only have a finite number of children the cardinalities are equal - N(M) = N(C). In the rather artificial case where a mother could have an infinite number of children, the inequality reappears. For it to be a strict inequality, you would need at least one mother having an infinite number of children of cardinality greater than the number of mothers. This is getting increasingly far from practical (it did that as soon as there were infinite numbers of any type)
A related fact about cardinal numbers is that if A and B are two cardinal numbers and at least one of them is infinite, then A * B = max(A, B).
Anyway, Elroch, cut it out. You're getting crazier and crazier. Only three months ago you were telling me that the stress on your threads was getting too much for you and you had an irregular heartbeat or something and next thing, you were picking quarrels with people again. Is it any wonder you're cracking up? I'm pretty sure you are on medication since when i knew you in my previous account circa 2011, you were batshoot crazy and regularly flew into rages and tantrums.
Yet another nonsense claim. I am not sure if you are making it up, imagining it or getting confused who said what.
Fortunately, I have never had any heart problems, I am a keen runner, which helps. I can reveal my resting heart rate was 46 for 3 consecutive days this week before going up to 47 yesterday. The lowest it has ever been is 42. I have not had any need to take any medication for many years (except vaccinations) and very little ever, fortunately.
Don't worry, I am sure @DiogenesDue is as completely unconcerned by you disliking him as I am.
The whole of the bleedin site that knows you knows you're a would-be bully and you're dishonest. The fact is that you are far more "concerned" by me than I am by you. Goodnight.
Yet another nonsense claim. Fortunately, I have never had any heart problems, I am a keen runner, which helps. I can reveal my resting heart rate was 46 for 3 consecutive days before going up to 47 yesterday. The lowest it has ever been is 42.
So you were lying on your thread three months ago? The thing is, I'm not sure I believe it was a lie because your behaviour is more and more that of a crazy person.
Regarding two infinite lists, one being larger, that is impossible for the reason that infinity is not finite.
This makes no sense. Let me explain how what you claim to be impossible is done. You define a partial order of size (cardinality) on sets as follows. If A and B are sets:
A <= B if there is a 1-1 mapping from A to B (i.e. A is in bijection with a subset of B).
This relation is easily proven to be transitive and reflexive, so it provides us with a partial order of magnitudes (sizes) of sets.
With more rigorous work we can generate the hierarchy of cardinalities, starting with the familar order of the sizes of finite sets, then moving to the size of the natural numbers - the first infinite (cardinal) number, and to larger infinity numbers.
You may believe that infinite numbers can't be different sizes, but the definitions and simply deduction prove otherwise. See any first year maths course for the details. (Or I can provide them).
If it is not finite, then it cannot be quantified
See above for how to do this.
and therefore one list cannot be shown to be larger.
And this.
Again, it might be ambiguous.
It's 100% unambiguous.
It can conceivably be both larger and not larger,
You might guess so. You would be wrong. The theorems based on the definitions prove otherwise.
depending on perspective, just as 0/0 is both 0 and 1
No. 0/0 is undefined.
If you can understand that, I'll talk to you some more. If you can't understand it, it would be hard work.
I understand it. You need a basic course on the subject.