Mummy, Mummy, what’s Russell’s Paradox?
Posted: Fri Dec 15, 2017 9:21 pm
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I'm well out of my depth with respect to Mathematics but I thought the ground for sets with respect to numbers was zero or { }, i.e. the empty set?Eodnhoj7 wrote:I never understood how sets could be observed as the foundation of number theory when the set, in itself, is "1". ...
Then what is the set? So the set is empty, that means the set exists. I am not arguing against you, but the logic for set theory requires the set to act like a "vessel" of number that is equivalent to one. What is the vessel but "1"?Arising_uk wrote: ↑Mon Dec 18, 2017 1:07 amI'm well out of my depth with respect to Mathematics but I thought the ground for sets with respect to numbers was zero or { }, i.e. the empty set?Eodnhoj7 wrote:I never understood how sets could be observed as the foundation of number theory when the set, in itself, is "1". ...
Does zero exist?Eodnhoj7 wrote:Then what is the set? So the set is empty, that means the set exists. ...
Zero, it is an empty set.I am not arguing against you, but the logic for set theory requires the set to act like a "vessel" of number that is equivalent to one. What is the vessel but "1"?
Arising_uk wrote: ↑Mon Dec 18, 2017 2:08 pmDoes zero exist?Eodnhoj7 wrote:Then what is the set? So the set is empty, that means the set exists. ...
It is not "anything". The observation of 0 is an observation of non-existence, which can only be observed relative to one.
Zero, it is an empty set.I am not arguing against you, but the logic for set theory requires the set to act like a "vessel" of number that is equivalent to one. What is the vessel but "1"?
I think this idea of a "vessel" misleading as a set, as far as I can tell, is just a group of things with no need to put them in an actual box.
But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
It can be relative to the absence of any number of things?Eodnhoj7 wrote:It is not "anything". The observation of 0 is an observation of non-existence, which can only be observed relative to one.
And in all cases there is no thing around them, just lots of objects?But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
According to set theory it has to be further sets, unless there is something I am missing.Arising_uk wrote: ↑Tue Dec 19, 2017 1:17 amIt can be relative to the absence of any number of things?Eodnhoj7 wrote:It is not "anything". The observation of 0 is an observation of non-existence, which can only be observed relative to one.
Relation is absence of structure. We can observe zero as the limit of 1 as "non-being" is the limit of being. This duality between 1 as "being" and 0 as "nonbeing" allows a synthesis as gradation or "deficiency" which we observe in fractals and negative numbers.
And in all cases there is no thing around them, just lots of objects?But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
Nothing about 1 and 0 leads to fractals nor negative numbers I'd have thought? As none of these things exist.Eodnhoj7 wrote:Relation is absence of structure. We can observe zero as the limit of 1 as "non-being" is the limit of being. This duality between 1 as "being" and 0 as "nonbeing" allows a synthesis as gradation or "deficiency" which we observe in fractals and negative numbers. ...
No idea as like I say mathematics not my thing but you said sets needed '1' to be the foundation of numbers and from what I can grasp they need '0' not '1' to define numbers.According to set theory it has to be further sets, unless there is something I am missing.But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
The set as empty may be zero {0}, but what about the set itself { }? If it is not a number, but a function of number, it needs a form to extend from, in this case "1". Zero is not a foundation, because zero is nothing. I understand that is what they may argue, but it is irrational as zero is absent of an definition.Arising_uk wrote: ↑Tue Dec 19, 2017 4:26 amNothing about 1 and 0 leads to fractals nor negative numbers I'd have thought? As none of these things exist.Eodnhoj7 wrote:Relation is absence of structure. We can observe zero as the limit of 1 as "non-being" is the limit of being. This duality between 1 as "being" and 0 as "nonbeing" allows a synthesis as gradation or "deficiency" which we observe in fractals and negative numbers. ...
elaborate your point.
No idea as like I say mathematics not my thing but you said sets needed '1' to be the foundation of numbers and from what I can grasp they need '0' not '1' to define numbers.According to set theory it has to be further sets, unless there is something I am missing.But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
Again, not my field but from what I see { } is the empty set, {0} is 1 in numbers so they appear to think zero is a number and given it is a number symbol I guess they are correct?Eodnhoj7 wrote:The set as empty may be zero {0}, but what about the set itself { }? If it is not a number, but a function of number, it needs a form to extend from, in this case "1". Zero is not a foundation, because zero is nothing. I understand that is what they may argue, but it is irrational as zero is absent of an definition.
http://www.straightdope.com/columns/rea ... -a-number/Arising_uk wrote: ↑Tue Dec 19, 2017 4:33 amAgain, not my field but from what I see { } is the empty set, {0} is 1 in numbers so they appear to think zero is a number and given it is a number symbol I guess they are correct?Eodnhoj7 wrote:The set as empty may be zero {0}, but what about the set itself { }? If it is not a number, but a function of number, it needs a form to extend from, in this case "1". Zero is not a foundation, because zero is nothing. I understand that is what they may argue, but it is irrational as zero is absent of an definition.
I think you're on shaky ground if you are looking to provide a foundation for Mathematics as Russell and Whitehead tried with Logic and only partly succeeded, mainly with the numbers as it happened.Eodnhoj7 wrote:Thats the thing, some people say zero is a number and others say it is not. One is a number, plus it provides a foundation. ...
What are numbers in our Mathematics, functions. What do you think they are?Would zero be a number without the set? ...
Not sure what you mean here but, as best I understand it, a set doesn't have to be a number as it can be the empty set { }.That is the question I ask, because if it requires a set to be a number than the set itself must be a number conducive to one.