No sets of numbers

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There are no members in the set 'a set of even numbers'. A number is a number in a mathematical application. As the properties of the members of a set do not confer their properties on the set, then the members of the set 'the set of even numbers' are not counted. Accordingly the set 'the set of even numbers' has no members.

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The set of even integers is a group.

Rap

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raprap wrote:

The set of even integers is a group.

Rap

Neither a group nor a set of integers are composed of integers.

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John Jones wrote:

raprap wrote:
The set of even integers is a group.

Rap

Neither a group nor a set of integers are composed of integers.

You've sealed the display of your arbitrary ignorance. It has become blatantly obvious you have not the concept of 'clearly defined', the meaning of 'set' and/or 'the meaning of group.'

A 'group' is a 'set' that has clearly defined properties, it is closed under addition, it has a unique identity that is a member of the set, and each set element has a unique inverse that are also members of the set. In this case the group is also abelian, named after the 19th century mathematician Abel that defined, developed and 'clearly defined' groups and the properties of groups.

If I were you, I would move my contrite comments to some forum other than science and mathematics because it does not belong here. Exclamation

Rap

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raprap wrote:

John Jones wrote:
raprap wrote:
The set of even integers is a group.

Rap

Neither a group nor a set of integers are composed of integers.

You've sealed the display of your arbitrary ignorance. It has become blatantly obvious you have not the concept of 'clearly defined', the meaning of 'set' and/or 'the meaning of group.'

A 'group' is a 'set' that has clearly defined properties, it is closed under addition, it has a unique identity that is a member of the set, and each set element has a unique inverse that are also members of the set. In this case the group is also abelian, named after the 19th century mathematician Abel that defined, developed and 'clearly defined' groups and the properties of groups.

If I were you, I would move my contrite comments to some forum other than science and mathematics because it does not belong here.

Rap

Oh dear, the mathematicians are outraged again. Someone rocked their boat. Pathetic.

A set doesn't have properties conferred on it by its members. So, how does a set 'have' properties? If I were you I would respond to an argument straight-forwardly, instead of pushing out some old bloated goat in his flaming gondola. A set doesn't have properties conferred on it by its members. A set doesn't have properties conferred on it by its members. So, how does a set 'have properties'? So, how does a set 'have properties'?

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I'm not a mathematician, I'm an Engineer. But I know enough mathematics to know that if you ran up an alley yelling "Fish!" it would make more sense that what you've posted here.

Rap c∫;?/

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raprap wrote:

I'm not a mathematician, I'm an Engineer. But I know enough mathematics to know that if you ran up an alley yelling "Fish!" it would make more sense that what you've posted here.

Rap c∫;?/

Shutup.

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Re: No sets of numbers
Furthermore, the idea that a set has properties allows us to infer rather than construct sub-sets. But a set does not have the properties of its 'members' conferred on the set. It follows that a set cannot use the properties of the members of the set to create a set or sub-set as the set cannot recognise properties. If follows that 'sub-sets' are created 'outside' the set and cannot be inferred. They are not a part of the set's remit as a referencing agent, unless they are included specifically in the name of the set. But if they are included in the name of the set then there is only the set. We can discard the idea of 'sub-sets' and make appropriate adjustments to theory elsewhere.

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John Jones wrote:

raprap wrote:
I’m not a mathematician, I’m an Engineer. But I know enough mathematics to know that if you ran up an alley yelling “Fish!” it would make more sense that what you’ve posted here.

Rap c∫;?/

Shutup.

Oh dear, the "philosopher" is getting testy.

Hey everybody, maybe if we ignore this @$$, he'll go away. Or, we could reply to each of his nonsense posts with a philosopher joke.

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JJ - you've maybe confused the words group and set with a mathematically field, and word member with the generators of a set or field.

Either that or you have a quantity of conciousness enhancement substances.

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g__day wrote:

JJ - Either that or you have a quantity of conciousness enhancement substances.

No, its philosophy. Tuck your vest into your trousers.

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A set of objects is only a set of objects if the objects are named. Otherwise, we have to assume that the properties of the world are conferred on the set. The property of the world that is assumed by the set 'the set of objects' is that objects can present themselves. However, objects do not present themselves but, like the symbolism and functions of mathematics, are arbitrarily constructed.

So there is a problem. This limitation of sets - that properties of the members of the set cannot be conferred on the set, is obviated by the 'group'. Here, the members of the group have a relationship with each other, which they do not have in the set. As they have a relationship with each other the properties of the members of the group are conferred on the group.

This is the fundamental difference between a set and a group.

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Philosophy - that's about 8 forums below this one, perhaps you got lost on your way in? This is Science and Mathematics last I looked!

Mixing philosophy and mathematics is like combining chain saws and camels - okay if you're into that sort of thing. Have you ever heard of the expression (translated) painting the tiger and chasing the fence - a fruitless, difficult and sometimes dangerous task that makes those wonder why a man would pursue it (borrowed from Monkey)!

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g__day wrote:

Philosophy - that's about 8 forums below this one, perhaps you got lost on your way in? This is Science and Mathematics last I looked!

Mixing philosophy and mathematics is like combining chain saws and camels - okay if you're into that sort of thing. Have you ever heard of the expression (translated) painting the tiger and chasing the fence - a fruitless, difficult and sometimes dangerous task that makes those wonder why a man would pursue it (borrowed from Monkey)!

It takes a philospher to define 'number'. Mathematicians are technicians. They would not know where to start. Their trade is symbols and patterns which they learn mechanically, that is, which they learn mathmatically.

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While the philosophers are tripping over their egos in an attempt to properly define 'number' and maintain their 'rightful' position above all other disciplines, the lowly technicians are busy discovering new and wonderful things about numbers - many of which benefit a variety of other disciplines.

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One of the last renowned philosophers who claimed science as his bailiwick was Aristotle. It took almost 2000 years and technicians like Newton, Galileo and Copernicus to partially undo the philosophical fantasies of Aristotelian science and logic (ID is IMO a remnant of Aristotle).

Philosophy has turned out to be a real nice entertainment and somewhat useful in the fields of religion, and law, and morality, but it doesn't add caloric input for the hydrogenation of fats. It has taken countless thousands of brilliant technicians to do that.

Rap c∫;?/

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Mathematics is the mapping of metaphysical objects to number and function. Without this mapping we do not have mathematics. Most mathematicians mistakenly concern themselves with number and function only, and casually let slide the metaphysical concerns to common myth. Sets can provide us with a good example where this type of mistake is made. The fact that mathematicians think that number can be presented in the absence of application demonstrates a mistake of metaphysics. A bag of numbers are not numbers but merely shapes. It follows that a set of numbers is not a set of numbers. Mathematicians need to understand how mathematics is constructed, and not mistake the 'working' content for the structure.

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No sets of numbers

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