Re: Is the empty set a number?
- From: jonas.thornvall@xxxxxxxxxxx
- Date: Thu, 10 Apr 2008 22:43:41 -0700 (PDT)
On 10 Apr, 21:16, BuddhaThu <softspokenbud...@xxxxxxxxx> wrote:
Numbers are a type of naming in relation to things.
I agree
An empty set can only make sense in relation to other sets with a definable property.
Well here i am not sure i agree, in my mind the set only is a
container of a group and have no value on its own.
At least not a value that have numerical significance in relation to
the rational numbers.
In the same way color is not a member in of the group red, green,
blue, yellow it is only a definition in this case of the fact that
colors exist. Color in itself is nothing without the use of a member.
The expression number is the full set of all numbers, but the empty
set lack numbers. The empty set is only an abstract notion of the fact
we can group things in brackets or containers.
I am not sure i consider the set in itself a mathematical entity only
an abstract idea that we can define a group without members. (i am
pretty sure the set dont exist without members). The abstract idea of
no group exist though.
It does not make it a mathematical entity.
The empty set designated as '0' is 'even' in relation to the integer number line pointing to size i.e., -2,-1, 0, 1, 2, etc...
I do not consider 0 to be a number i consider it to be a human
invention to express the fact that the group have no members.
But I think what your question is whether an empty set can be considered a 'thing.'
No i consider the empty set to be a construct of human mind to express
absense, i am sure THE EMPTY SET is not a thing, and i doubt that it
is a NECESSARY mathematical entity.
The way i see it the human mind created logic and math to describe
grouprelations, without groups there would be no members no sets and
no math. Without groups there can not be THINGS but as soon you have a
member or a group YOU SURELY HAVE THINGS.
From the idea of NO THINGS... absense of group the empty set and thezero concept was developed.
Numbers are not things. None of the numbers are things. They are just abstract concepts to rigidly classify and name things in rigid order. When you name a group of rocks '3.' The rocks are not '3', but the rigid naming relying on the abstract concept of '3' is '3.'
Sure numbers are things, they are members of NUMBERS and have the
GROUP property used as proof of their thingyness. 0 is not a member of
numbers though.
Abstract concepts like numbers cannot exist alone. Despite being 'nouns', they must also act as 'predicates' in that they must hook onto something in relation to something else to make sense.
True is that they would be meaningless in a reality without things.
But if abstract intelligence can exist, the idea of NUMBERS can exist
once the concept is developed. So i am not against the idea of
abstract numbers itself only that 0 and empty set is members of
NUMBERS.
This is because they are abstract. While all predicates are abstract not all nouns are. So it is important to make the splice in nouns.
This 'hooking' can take place among other 'abstract objects' and/or evemtually relationshps to physical things. Otherwise, you end up with nasty metaphysical dangling participles like Plato.
I hope that I have adequately answered your question.
B.T.
JT
.
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- Is the empty set a number?
- From: jonas . thornvall
- Re: Is the empty set a number?
- From: BuddhaThu
- Is the empty set a number?
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