Chess will never be solved, here's why

The majority of the other people here understand that you were talking pure manure when you claimed that Cantor, an excellent mathematician, would suggest any entity would have a property and its negation simultaneously (in italics in an unedited quote from you above). It takes someone incompetent to come up with such a thing.

This is proven by the impossibility of you providing any source to support the ridiculous claim about Cantor.

You must be looking in a mirror, then...

The notion that if your son deigned to comment here that this would call for you to exit the thread is just bizarre, by the way. Sounds more like a poor attempt to explain away something uncomfortable.

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

"My son, so far as I know, has never commented on the forums. If he did join in, I'd stop right away"
Assuming the 'son' exists - then O wouldn't want the son to see his posts - for obvious reasons.
And the idea that O would be 'right' more often than Elroch in their exchanges is ridiculous. It that a lie or a delusion by O?
Its very possible that O has not been right even once - not even once at all in exchanges with Elroch and Dio and Martin and mpaetz over a two to ten year period.
Except when O hasn't disagreed.

Very well put by mrh. Efficient logic.

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.

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.

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.

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.

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.

Reality check time.

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).

Don't worry, I am sure @DiogenesDue is as completely unconcerned by you disliking him as I am.

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.

No, @Optimissed.